{"id":31293,"date":"2022-04-02T10:44:27","date_gmt":"2022-04-02T05:14:27","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=31293"},"modified":"2022-04-07T11:33:49","modified_gmt":"2022-04-07T06:03:49","slug":"big-ideas-math-answers-grade-8-chapter-9","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-9\/","title":{"rendered":"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem"},"content":{"rendered":"<p>Redefine your true self using the Big Ideas Math Answers Grade 8 Ch 9 Real Numbers and the Pythagorean Theorem. Shed the inhibitions that are holding you back and begin your practice using the BIM Grade 8 Chapter 9 Solutions and clear the exam with better grades. <strong>Big Ideas Math Grade 8 Answers<\/strong> Chapter 9 Real Numbers and the Pythagorean Theorem is given as per the latest syllabus guidelines. Enhance your math skills by making the most out of the BIM Book Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem Solutions.<\/p>\n<h2>Big Ideas Math Book 8th Grade Answer Key Chapter 9 Real Numbers and the Pythagorean Theorem<\/h2>\n<p>Access the Topicwise Big Ideas Math Grade 8 Chapter 9 Real Numbers and Pythagorean Theorem Answers provided below via quick links. Help your child with the homework help he might need right after class and master the concepts. Kickstart your preparation taking the help of the BIM 8th Grade Ch 9 Real Numbers and Pythagorean Theorem Answer Key and identify the areas of need and allot time accordingly.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Real_Numbers_and_the_Pythagorean_Theorem_STEAM_Video\/Performance_Task\">Real Numbers and the Pythagorean Theorem STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Real_Numbers_and_the_Pythagorean_Theorem_Getting_Ready_for_Chapter_9\">Real Numbers and the Pythagorean Theorem Getting Ready for Chapter 9<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Finding Square Roots<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.1_Finding_Square_Roots\">Lesson 9.1 Finding Square Roots<\/a><\/li>\n<li><a href=\"#Finding_Square_Roots_Homework_&amp;_Practice_9.1\">Finding Square Roots Homework &amp; Practice 9.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 The Pythagorean Theorem<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.2_The_Pythagorean_Theorem\">Lesson 9.2 The Pythagorean Theorem<\/a><\/li>\n<li><a href=\"#The_Pythagorean_Theorem_Homework_&amp;_Practice_9.2\">The Pythagorean Theorem Homework &amp; Practice 9.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Finding Cube Roots<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.3_Finding_Cube_Roots\">Lesson 9.3 Finding Cube Roots<\/a><\/li>\n<li><a href=\"#Finding_Cube_Roots_Homework_&amp;_Practice_9.3\">Finding Cube Roots Homework &amp; Practice 9.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.4_Rational_Numbers\">Lesson 9.4 Rational Numbers<\/a><\/li>\n<li><a href=\"#Rational_Numbers_Homework_&amp;_Practice_9.4\">Rational Numbers Homework &amp; Practice 9.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Irrational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.5_Irrational_Numbers\">Lesson 9.5 Irrational Numbers<\/a><\/li>\n<li><a href=\"#Irrational_Numbers_Homework_&amp;_Practice_9.5\">Irrational Numbers Homework &amp; Practice 9.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 The Converse of the Pythagorean Theorem<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/@Lesson_9.6_The_Converse_of_the_Pythagorean_Theorem\">Lesson 9.6 The Converse of the Pythagorean Theorem<\/a><\/li>\n<li><a href=\"#The_Converse_of_the_Pythagorean_Theorem_Homework_&amp;_Practice_9.6\">The Converse of the Pythagorean Theorem Homework &amp; Practice 9.6<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 9 &#8211; Real Numbers and the Pythagorean Theorem<\/strong><\/p>\n<ul>\n<li><a href=\"#Real_Numbers_and_the_Pythagorean_Theorem_Connecting_Concepts\">Real Numbers and the Pythagorean Theorem Connecting Concepts<\/a><\/li>\n<li><a href=\"#Real_Numbers_and_the_Pythagorean_Theorem_Chapter_Review\">Real Numbers and the Pythagorean Theorem Chapter Review<\/a><\/li>\n<li><a href=\"#Real_Numbers_and_the_Pythagorean_Theorem_Practice_Test\">Real Numbers and the Pythagorean Theorem Practice Test<\/a><\/li>\n<li><a href=\"#Real_Numbers_and_the_Pythagorean_Theorem_Cumulative_Practice\">Real Numbers and the Pythagorean Theorem Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Real_Numbers_and_the_Pythagorean_Theorem_STEAM_Video\/Performance_Task\"><\/a>Real Numbers and the Pythagorean Theorem STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Metronome Design<br \/>\nA metronome is a device that ticks at a constant rate. A metronome includes a pendulum, which swings back and forth in a precise time called a period. Why do musicians use metronomes?<br \/>\nWatch the STEAM Video \u201cMetronome Design.\u201d Then answer the following questions. The equation T = 0.2\u221aL relates the period T (in seconds) and the length L (in centimeters) of a pendulum, where \u221aL is the square root of L.<br \/>\n1. The table shows the square roots of several values of L. Use the pattern to find the values of \u221a36 , \u221a49 , and \u221a64 .<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 1\" width=\"422\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-1.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-1-300x148.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><br \/>\n2. What is the period of a pendulum that is 100 centimeters long? Justify your answer.<\/p>\n<p>Answer:<br \/>\n1. \u221a36 = 6<br \/>\n\u221a49 = 7<br \/>\n\u221a64 = 8<br \/>\n2. \u221a100 = 10<\/p>\n<p>Explanation:<br \/>\nIn the above given table the square roots of 1,2, 3,4,5 are given<br \/>\nsquare root of 36 = 6<br \/>\n6 x 6 = 36<br \/>\nsquare root of\u00a0 49 = 7<br \/>\n7 x 7 =49<br \/>\nsquare root of\u00a0 64 = 8<br \/>\n8 x 8 =64<br \/>\n2. given that period of the pendulum is 100 centimeters.<br \/>\nsquare root of 100 =10<br \/>\n10 x 10 = 100<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Identify and Correct the Error!<br \/>\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the lengths of several pendulums.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 2\" width=\"579\" height=\"328\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-2.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-2-300x170.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><br \/>\nYou will be asked to identify and correct errors in calculations of periods. Why is it important to pay attention to units when substituting values into a formula?<\/p>\n<p>Answer:<br \/>\n0.438 sec, 1.219 sec, 1.612sec.<\/p>\n<p>Explanation:<br \/>\n1 feet = 0.3048 seconds<br \/>\nso in the question given that the length of 1.44= 1.44 x 0.3048 sec<br \/>\n0.438 sec<br \/>\n4 x 0.3048 = 1.219 sec<br \/>\n5.29 x 0.3048 = 1.612 sec.<\/p>\n<h3><a id=\"Real_Numbers_and_the_Pythagorean_Theorem_Getting_Ready_for_Chapter_9\"><\/a>Real Numbers and the Pythagorean Theorem Getting Ready for Chapter 9<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>When you multiply a number by itself, you square the number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 3\" width=\"380\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-3.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-3-300x48.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><br \/>\nTo\u201cundo\u201d this, take the square root of the number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 4\" width=\"460\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-4.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-4-300x47.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><br \/>\n1. Work with a partner. Find the radius of each circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 5\" width=\"476\" height=\"297\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-5.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-5-300x187.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Answer:<br \/>\na. 6 in<br \/>\nb. 1 yd<br \/>\nc. 0.5 ft<br \/>\nd. (3\/9) m<br \/>\ne. 0.7 cm<br \/>\nf. 1.2 in<\/p>\n<p>Explanation:<br \/>\na. The radius of circle = (\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\ngiven that area = 36 \u03c0 in\u00b2<br \/>\nradius = (\u221a 36 \u03c0 \/ \u03c0 )<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canclled.<br \/>\nradius = ( \u221a 36)<br \/>\nsquare root of 36 is 6 x 6<br \/>\n\u221a 36 = \u221a 6\u00b2<br \/>\nwhere square and square root get cancelled.<br \/>\nradius = 6 in<br \/>\nb. The radius of circle = (\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\ngiven that area = \u03c0 yd\u00b2<br \/>\nradius = (\u221a \u03c0 \/ \u03c0 )<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canceled.<br \/>\nradius = ( \u221a 1)<br \/>\nthe square root of 1 is 1 x 1<br \/>\n\u221a 1= \u221a 1\u00b2<br \/>\nwhere square and square root get canceled.<br \/>\nradius =1 yd<br \/>\nc. The radius of circle = (\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\ngiven that area = 0.25 \u03c0 ft<br \/>\nradius = (\u221a 0.25\u03c0 \/ \u03c0 )<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canceled.<br \/>\nradius = ( \u221a 0.25)<br \/>\nthe square root of 0.25 is 0.5 x 0.5<br \/>\n\u221a 0.25 = \u221a 0.5\u00b2<br \/>\nwhere square and square root get canceled.<br \/>\nradius = 0.5 ft<br \/>\nc. The radius of circle = (\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\ngiven that area = 0.25 \u03c0 ft<br \/>\nradius = (\u221a 0.25\u03c0 \/ \u03c0 )<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canceled.<br \/>\nradius = ( \u221a 0.25)<br \/>\nthe square root of 0.25 is 0.5 x 0.5<br \/>\n\u221a 0.25 = \u221a 0.5\u00b2<br \/>\nwhere square and square root get canceled.<br \/>\nradius = 0.5 ft<br \/>\nd. The radius of circle = (\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\ngiven that area = (9\/16) \u03c0 m\u00b2<br \/>\nradius = (\u221a (9\/16)\u03c0 \/ \u03c0 )<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canceled.<br \/>\nradius = ( \u221a (9\/16)<br \/>\nthe square root of (9\/16) is (3\/4) x (3\/4)<br \/>\n\u221a (9\/16) = \u221a (3\/4)\u00b2<br \/>\nwhere square and square root get canceled.<br \/>\nradius = (3\/4) m<br \/>\ne. The radius of circle = (\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\ngiven that area = (0.49) \u03c0cm\u00b2<br \/>\nradius = (\u221a (0.49)\u03c0 \/ \u03c0 )<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canceled.<br \/>\nradius = ( \u221a (0.49)<br \/>\nthe square root of (0.49) is (0.7) x (0.7)<br \/>\n\u221a (0.49) = \u221a (0.7)\u00b2<br \/>\nwhere square and square root get canceled.<br \/>\nradius = (0.7) cm<br \/>\nf. The radius of circle = (\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\ngiven that area = (1.44) \u03c0 in\u00b2<br \/>\nradius = (\u221a (1.44)\u03c0 \/ \u03c0 )<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canceled.<br \/>\nradius = ( \u221a (1.44)<br \/>\nthe square root of (1.44) is (1.2) x (1.2)<br \/>\n\u221a (1.44) = \u221a (1.2)\u00b2<br \/>\nwhere square and square root get canceled.<br \/>\nradius = (1.2) in<\/p>\n<p>2. <strong>WRITING GUIDELINES<\/strong> Work with a partner. Explain how you can find the radius and diameter of a circular object when you are given its area. Justify your answer using an example that is different from those in Exercise 1.<\/p>\n<p>Answer:<br \/>\nThe radius of circle = 8 cm<br \/>\nThe diameter of circle = 16 cm<\/p>\n<p>Explanation:<br \/>\nfor example, we have to consider the area of a circle is\u00a0 64\u03c0 cm\u00b2 given.<br \/>\nwe have to find the radius and diameter of the circle.<br \/>\nThe radius of circle = (\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\nthe radius of circle = (\u221a64\u03c0\/\u03c0)<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canceled.<br \/>\nradius = ( \u221a (64)<br \/>\nthe square root of (64) is (8) x (8)<br \/>\n\u221a (64) = \u221a (8)\u00b2<br \/>\nwhere square and square root get canceled.<br \/>\nradius = 8 cm<br \/>\nThe radius of circle = (2\u221aA\/\u03c0)<br \/>\nwhere A = area of a circle, \u03c0 = 3.14<br \/>\nthe radius of circle = (2\u221a64\u03c0\/\u03c0)<br \/>\nboth in the numerator and denominator \u03c0\u00a0 get canceled.<br \/>\ndiameter = ( 2\u221a (64)<br \/>\nthe square root of (64) is (8) x (8)<br \/>\n\u221a (64) = 2\u221a (8)\u00b2<br \/>\nwhere square and square root get canceled.<br \/>\ndiameter = 2 x 8 cm<br \/>\ndiameter = 16 cm<br \/>\n<strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are defined in this chapter. Think about what the terms might mean and record your thoughts.<br \/>\nsquare root<br \/>\ncube root<br \/>\nirrational number<br \/>\nperfect square<br \/>\nperfect cube<\/p>\n<p>Answer:<br \/>\nsquare root = a number that produces a specified quantity when multiplied by itself.<br \/>\ncube root = the number which produces a given number when cubed.<br \/>\nirrational number = an irrational number is a number that cannot be expressed as a fraction for any integers.<br \/>\nperfect square = perfect square is another term for square number.<br \/>\nperfect cube = a perfect cube is an integer that is equal to some other integer raised to the third power<br \/>\nsquare root\u00a0 of 36<\/p>\n<p>Explanation:<br \/>\n36 = 6 x 6<br \/>\n\u221a 36 = \u221a 6 \u00b2<br \/>\nwhere square and square root get canceled.<br \/>\n36 = 6<br \/>\ncube root of 343<br \/>\n343 = 7 x 7 x 7<br \/>\n3\u221a 343 = \u221a 7\u00a0 \u00b3<br \/>\nwhere cube and cube root get canceled.<br \/>\n343 = 7<br \/>\nirrational number<br \/>\nExample : \u221a 2, \u221a 3, \u221a 5, \u221a 11, \u221a 12, \u03c0 (pi) are\u00a0 all irrational.<br \/>\nperfect square<br \/>\n9 = 3 x 3<br \/>\nperfect cube<br \/>\n125 = 5 x 5 x 5<\/p>\n<h3><a id=\"Lesson_9.1_Finding_Square_Roots\"><\/a>Lesson 9.1 Finding Square Roots<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding Side Lengths<br \/>\nWork with a partner. Find the side length of each square. Explain your method.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 1\" width=\"472\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-1.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-1-300x208.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Answer:<br \/>\na. 9yd<br \/>\nb. 18 cm<br \/>\nc. 19 mi<br \/>\nd. 15 mi<br \/>\ne. 1.7 in<br \/>\nf. 0.2 ft<\/p>\n<p>Explanation:<br \/>\nArea of a square = a \u00b2<br \/>\nwhere a = side<br \/>\nGiven that A = 81yd \u00b2<br \/>\nA = s x s<br \/>\nA = 9 x 9<br \/>\na = 9<br \/>\nb.Given that A =324cm \u00b2<br \/>\nA = s x s<br \/>\nA = 18 x 18<br \/>\na = 18 cm<br \/>\nc. Given that A =361 mi \u00b2<br \/>\nA = s x s<br \/>\nA = 19 x 19<br \/>\na = 19 mi<br \/>\nd. Given that A =225 mi\u00b2<br \/>\nA = s x s<br \/>\nA = 15 x 15<br \/>\na = 15 mi<br \/>\ne. Given that A =2.89in \u00b2<br \/>\nA = s x s<br \/>\nA = 1.7 x 1.7<br \/>\na = 1.7 in<br \/>\nf. Given that A =(4\/9) ft \u00b2<br \/>\nA = s x s<br \/>\nA = (2\/3) x (2\/3)<br \/>\na = (2\/3) ft<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding Solutions of Equations<br \/>\nWork with a partner. Use mental math to solve each equation. How many solutions are there for each equation? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 2\" width=\"560\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-2.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-2-300x86.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Answer:<br \/>\nx = +0, -0<br \/>\nx = +1, -1<br \/>\nx = +2, -2<br \/>\nx = +3, -3<br \/>\nx = +4, -4<br \/>\nx = +5, -5<\/p>\n<p>Explanation:<br \/>\nx\u00b2 = 0, x = +0, -0<br \/>\nx\u00b2 = 1, x =+1, -1<br \/>\nx\u00b2 = 4, x = +2, -2<br \/>\nx\u00b2 = 9, x = +3, -3<br \/>\nx\u00b2 = 16, x = +4, -4<br \/>\nx\u00b2 = 25, x = +5, -5<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 3\" width=\"187\" height=\"113\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the two square roots of the number.<\/strong><br \/>\nQuestion 1.<br \/>\n36<\/p>\n<p>Answer:<br \/>\n6 , -6<\/p>\n<p>Explanation:<br \/>\nsquare root of 36 = 6x 6<br \/>\n6 and -6<\/p>\n<p>Question 2.<br \/>\n100<\/p>\n<p>Answer:<br \/>\n10 , &#8211; 10<\/p>\n<p>Explanation:<br \/>\nsquare root of 100 = 10 x 10<br \/>\n10 and &#8211; 10<\/p>\n<p>Question 3.<br \/>\n121<\/p>\n<p>Answer:<br \/>\n11,\u00a0 &#8211; 11<\/p>\n<p>Explanation:<br \/>\nsquare root of 121 = 11 x 11<br \/>\n11 and &#8211; 11<\/p>\n<p><strong>Find the square root(s).<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\sqrt{4}\\)<\/p>\n<p>Answer:<br \/>\n2<\/p>\n<p>Explanation:<br \/>\nsquare root of 4 = 2 x 2<br \/>\n2<\/p>\n<p>Question 5.<br \/>\n&#8211; \\(\\sqrt{81}\\)<\/p>\n<p>Answer:<br \/>\n9<\/p>\n<p>Explanation:<br \/>\nsquare root of 81 = 9 x 9<br \/>\n9<\/p>\n<p>Question 6.<br \/>\n\u00b1 \\(\\sqrt{64}\\)<\/p>\n<p>Answer:<br \/>\n8<\/p>\n<p>Explanation:<br \/>\nsquare root of 64 = 8 x 8<br \/>\n8<\/p>\n<p><strong>Find the square root(s).<\/strong><br \/>\nQuestion 7.<br \/>\n&#8211; \\(\\sqrt{\\frac{1}{100}}\\)<\/p>\n<p>Answer:<br \/>\n&#8211; 0.1<\/p>\n<p>Explanation:<br \/>\nsquare root of (1\/100) = (1\/10 x 10)<br \/>\n(1\/10) = 0.1<br \/>\n&#8211; 0.1<\/p>\n<p>Question 8.<br \/>\n\u00b1 \\(\\sqrt{\\frac{4}{25}}\\)<\/p>\n<p>Answer:<br \/>\n\u00b1 0.4<\/p>\n<p>Explanation:<br \/>\nsquare root of (4\/25) = 0.16<br \/>\n0.16 = 0.4 x 0.4<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt{12.25}\\)<\/p>\n<p>Answer:<br \/>\n3.5<\/p>\n<p>Explanation:<br \/>\nsquare root of (12.25) = 3.5<br \/>\n12.25 = 3.5 x 3.5<\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 10.<br \/>\n12 &#8211; 3\\(\\sqrt{25}\\)<\/p>\n<p>Answer:<br \/>\n-3<\/p>\n<p>Explanation:<br \/>\nsquare root of 25 = 5<br \/>\n12 &#8211; 3 (5)<br \/>\n12 &#8211; 15<br \/>\n-3<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt{\\frac{28}{7}}\\) + 2.4<\/p>\n<p>Answer:<br \/>\n4.4<\/p>\n<p>Explanation:<br \/>\n(28\/7) = 4<br \/>\nsquare root of 4 = 2<br \/>\n2 + 2.4<br \/>\n4.4<\/p>\n<p>Question 12.<br \/>\n15 &#8211; (\u221a4)<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n11<\/p>\n<p>Explanation:<br \/>\nsquare root of 16\u00a0 = 4<br \/>\n15 &#8211; 4<br \/>\n11<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 13.<br \/>\nk<sup>2<\/sup> = 169<\/p>\n<p>Answer:<br \/>\nk = 13<\/p>\n<p>Explanation:<br \/>\nsquare root of 169 = 13 x 13<br \/>\nk = 13<\/p>\n<p>Question 14.<br \/>\n7n<sup>2<\/sup> = 175<\/p>\n<p>Answer:<br \/>\nn = 5<\/p>\n<p>Explanation:<br \/>\nn\u00b2 = (175\/7)<br \/>\nn = 25<br \/>\nsquare root of 25\u00a0 = 5 x 5<br \/>\nn = 5<\/p>\n<p>Question 15.<br \/>\n190 = 4b<sup>2<\/sup> &#8211; 6<\/p>\n<p>Answer:<br \/>\nb = 7<\/p>\n<p>Explanation:<br \/>\n190 = 4b<sup>2<\/sup> &#8211; 6<br \/>\n<sup><span style=\"font-size: 16px;\">4b\u00b2\u00a0= 190 + 6<br \/>\n<\/span> <span style=\"font-size: 16px;\">4b\u00b2=196<br \/>\n<\/span><\/sup>b<sup><span style=\"font-size: 16px;\">\u00b2 = (196\/4)<br \/>\nb\u00b2 = 49<br \/>\nb = 7<\/span><\/sup><\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>FINDING SQUARE ROOTS <\/strong>Find the square root(s).<br \/>\nQuestion 16.<br \/>\n\\(\\sqrt{256}\\)<\/p>\n<p>Answer:<br \/>\n16<\/p>\n<p>Explanation:<br \/>\nsquare root of 256\u00a0 = 16 x 16<br \/>\n16<\/p>\n<p>Question 17.<br \/>\n&#8211; \\(\\sqrt{\\frac{1}{9}}\\)<\/p>\n<p>Answer:<br \/>\n&#8211; (1\/3)<\/p>\n<p>Explanation:<br \/>\nsquare root of (1\/9)\u00a0 = (1\/3)<br \/>\nsquare root of 9 = 3 x 3<br \/>\ngiven in &#8211; ve symbol<br \/>\n&#8211; (1\/3)<\/p>\n<p>Question 18.<br \/>\n\u00b1 \\(\\sqrt{1.44}\\)<\/p>\n<p>Answer:<br \/>\n\u00b1 1.2<\/p>\n<p>Explanation:<br \/>\nsquare root of 1.44 = 1.2<br \/>\nsquare root of 1.44 = 1.2 x 1.2<br \/>\ngiven in \u00b1 symbol<br \/>\n\u00b1 1.2<\/p>\n<p><strong>EVALUATING EXPRESSIONS <\/strong>Evaluate the expression.<br \/>\nQuestion 19.<br \/>\n\\(\\sqrt{\\frac{81}{9}}\\) &#8211; 7<\/p>\n<p>Answer:<br \/>\n&#8211; 4<\/p>\n<p>Explanation:<br \/>\nsquare root of 81 = 9 x 9<br \/>\nsquare root of\u00a0 9 = 3x\u00a0 \u00a03<br \/>\n(9\/3) = 3<br \/>\n3 &#8211; 7 = -4<\/p>\n<p>Question 20.<br \/>\n&#8211; 1 &#8211; \\(\\sqrt{121}\\)<\/p>\n<p>Answer:<br \/>\n-12<\/p>\n<p>Explanation:<br \/>\nsquare root of 121\u00a0 = 11 x 11<br \/>\n&#8211; 1 &#8211; 11<br \/>\n&#8211; 12<\/p>\n<p>Question 21.<br \/>\n5 + (\\(\\sqrt{2}\\))<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n7<\/p>\n<p>Explanation:<br \/>\nsquare root of 4\u00a0 \u00a0= 2 x 2<br \/>\n5 + 2<br \/>\n7<\/p>\n<p>SOLVING EQUATIONS Solve the equation.<br \/>\nQuestion 22.<br \/>\n2r<sup>2<\/sup> = 162<\/p>\n<p>Answer:<br \/>\nr = 9<\/p>\n<p>Explanation:<br \/>\n2r<sup>2<\/sup> = 162<br \/>\nr \u00b2 = (162\/2)<br \/>\nr\u00b2 = 81<br \/>\nsquare root of 81\u00a0 \u00a0= 9 x 9<br \/>\nr = 9<\/p>\n<p>Question 23.<br \/>\nd<sup>2<\/sup> + 5 = 41<\/p>\n<p>Answer:<br \/>\nd = 6<\/p>\n<p>Explanation:<br \/>\nd<sup>2<\/sup> + 5 = 41<br \/>\nd \u00b2 = 41 &#8211; 5<br \/>\nd \u00b2\u00a0 = 36<br \/>\nsquare root of 36\u00a0 \u00a0= 6 x 6<br \/>\nd = 6<\/p>\n<p>Question 24.<br \/>\n&#8211; 42 = 7b<sup>2<\/sup> &#8211; 385<\/p>\n<p>Answer:<br \/>\nb = &#8211; 7<\/p>\n<p>Explanation:<br \/>\n&#8211; 42 = 7b<sup>2<\/sup> &#8211; 385<br \/>\n7b \u00b2\u00a0 = &#8211; 385 + 42<br \/>\n7b \u00b2\u00a0 = &#8211; 343<br \/>\nb \u00b2\u00a0 = (- 343\/7)<br \/>\nb \u00b2\u00a0 = &#8211; 49<br \/>\nsquare root of\u00a0 &#8211; 49 = 7 x 7<br \/>\nb = &#8211; 7<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 25.<br \/>\nYour distance d (in miles) from the horizon can be approximated by d = 1.22\u221ah, where h is your eye level (in feet above ground level). What is your eye level when you are 9.76 miles from the horizon?<\/p>\n<p>Answer:<br \/>\nThe eye level when you are 9.76 miles from the horizon = 11.907 ft<\/p>\n<p>Explanation:<br \/>\nGiven that the horizon can be approximated by 1.22 feet<br \/>\nso 1.22 x 11.907<br \/>\n11.907 ft<br \/>\nthe eye level when you are 9.76 miles from the horizon = 11.907 ft.<\/p>\n<p>Question 26.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe speed s (in meters per second) of a tsunami can be modeled by the function s = \u221a9.8d, where d is the water depth (in meters).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 4\" width=\"168\" height=\"147\" \/><br \/>\na.What is the speed of the tsunami when the water depth is 500 meters?<br \/>\nb. What happens to the speed of the tsunami as the depth decreases? Explain.<\/p>\n<p>Answer:<br \/>\na. The speed of tsunami\u00a0 = 4,900 sq meters.<br \/>\nb. if the speed of the tsunami as depth decreases it has low flow.<\/p>\n<p>Explanation:<br \/>\na. Given that the speed of the tsunami = \u221a9.8d<br \/>\n\u221a9.8 x 500 where d = 500 given<br \/>\n4,900 sq meters<br \/>\nb. if the speed of the tsunami as depth decreases the flow of the water is also less.<\/p>\n<h3><a id=\"Finding_Square_Roots_Homework_&amp;_Practice_9.1\"><\/a>Finding Square Roots Homework &amp; Practice 9.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Evaluate the expression. Write your answer in scientific notation.<\/strong><br \/>\nQuestion 1.<br \/>\n(4.3 \u00d7 10<sup>3<\/sup>) + (2.4 \u00d7 10<sup>3<\/sup>)<\/p>\n<p>Answer<br \/>\n6.7 x 10 \u00b3<\/p>\n<p>Explanation:<br \/>\n(4.3 \u00d7 10<sup>3<\/sup>) + (2.4 \u00d7 10<sup>3<\/sup>)<br \/>\n(4.3 + 2.4) x 10\u00b3<br \/>\n6.7 x 10 \u00b3<\/p>\n<p>Question 2.<br \/>\n(1.5 \u00d7 10<sup>-2<\/sup>) &#8211; (3.5 \u00d7 10<sup>-3<\/sup>)<\/p>\n<p>Answer:<br \/>\n2 \u00d7 10<sup>-2<\/sup><\/p>\n<p>Explanation:<br \/>\n(1.5 \u00d7 10<sup>-2<\/sup>) &#8211; (3.5 \u00d7 10<sup>-3<\/sup>)<br \/>\n(1.5 &#8211; 3.5) x 10<sup>-2<\/sup><sup><br \/>\n<\/sup>2 \u00d7 10<sup>-2<\/sup><\/p>\n<p>Question 3.<br \/>\n9 \u00d7 (7 \u00d7 10<sup>-2<\/sup>)<\/p>\n<p>Answer:<br \/>\n6.3 x\u00a0 10 <sup> \u207b<\/sup>\u00b9<\/p>\n<p>Explanation:<br \/>\n9 \u00d7 (7 \u00d7 10<sup>-2<\/sup>)<br \/>\n(9 x 10) x 10<sup>-2<br \/>\n<\/sup>6.3 x\u00a0 10 <sup> \u207b<\/sup>\u00b9<\/p>\n<p>Question 4.<br \/>\n(6.6 \u00d7 10<sup>-5<\/sup>) \u00f7 (1.1 \u00d7 10<sup>4<\/sup>)<\/p>\n<p>Answer:<br \/>\n6 x 10<sup>-5<\/sup><\/p>\n<p>Explanation:<br \/>\n(6.6 \u00d7 10<sup>-5<\/sup>) \u00f7 (1.1 \u00d7 10<sup>4<\/sup>)<br \/>\n(6.6\/ 1.1) x 10<sup>-5<\/sup><br \/>\n6 x 10<sup>-5<\/sup><\/p>\n<p><strong>Make a scatter plot of the data. Identify any outliers, gaps, or clusters.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 5\" width=\"506\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-5.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-5-300x35.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Geometric-shapes-and-angles-9.1-1.png\" alt=\"\" width=\"513\" height=\"454\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Geometric-shapes-and-angles-9.1-1.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Geometric-shapes-and-angles-9.1-1-300x265.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Explanation:<br \/>\noutliers = (8,33) and (9,36)<br \/>\ngap = 3.5 meters to 8 meters.<br \/>\nfillers=2 meters to 3 meters.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 6\" width=\"503\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-6.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-6-300x41.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Geometric-shapes-and-angles-9.1-2.png\" alt=\"\" width=\"516\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Geometric-shapes-and-angles-9.1-2.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Geometric-shapes-and-angles-9.1-2-300x276.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Explanation:<br \/>\noutliers = (1,4.05) and (1, 4.00)<br \/>\ngap = 0.5 gallons to 1 gallon<br \/>\nfillers =1meter to 1.5 meters.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>FINDING SIDE LENGTHS<\/strong> Find the side length s of the square. (See Exploration 1, p. 373.)<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 7\" width=\"125\" height=\"151\" \/><\/p>\n<p>Answer:<br \/>\nS = 21 cm<\/p>\n<p>Explanation:<br \/>\nArea = 441 cm\u00b2<br \/>\nArea of square = a \u00b2<br \/>\nwhere a = side<br \/>\nsquare root of 441 = 21 x 21<br \/>\nside length = 21<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 8\" width=\"122\" height=\"148\" \/><\/p>\n<p>Answer:<br \/>\nS = 1.3 km<\/p>\n<p>Explanation:<br \/>\nArea = 1.69 km\u00b2<br \/>\nArea of square = a \u00b2<br \/>\nwhere a = side<br \/>\nsquare root of 1.69 = 1.3 x 1.3<br \/>\nside length = 1.3km<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 9\" width=\"143\" height=\"140\" \/><\/p>\n<p>Answer:<br \/>\nS = (6\/7) yd<\/p>\n<p>Explanation:<br \/>\nArea = (36\/49)\u00b2<br \/>\nArea of square = a \u00b2<br \/>\nwhere a = side<br \/>\nsquare root of (36\/49) = (6\/7) x (6\/7)<br \/>\nside length =(6\/7) yd<\/p>\n<p><strong>FINDING SQUARE ROOTS OF A PERFECT SQUARE<\/strong> Find the two square roots of the number.<br \/>\nQuestion 10.<br \/>\n9<\/p>\n<p>Answer:<br \/>\n3, &#8211; 3<\/p>\n<p>Explanation:<br \/>\nsquare root of 9 = 3 x 3<br \/>\n3<br \/>\ngiven that two square roots<br \/>\n3, -3<\/p>\n<p>Question 11.<br \/>\n64<\/p>\n<p>Answer:<br \/>\n8, &#8211; 8<\/p>\n<p>Explanation:<br \/>\nsquare root of 64 = 8 x 8<br \/>\n8<br \/>\ngiven that two square roots<br \/>\n8, -8<\/p>\n<p>Question 12.<br \/>\n4<\/p>\n<p>Answer:<br \/>\n2, -2<\/p>\n<p>Explanation:<br \/>\nsquare root of 4 = 2 x 2<br \/>\n2<br \/>\ngiven that two square roots<br \/>\n2, -2<\/p>\n<p>Question 13.<br \/>\n144<\/p>\n<p>Answer:<br \/>\n12, -12<\/p>\n<p>Explanation:<br \/>\nsquare root of 144 = 12 x 12<br \/>\n12<br \/>\ngiven that two square roots<br \/>\n12, -12<\/p>\n<p><strong>FINDING SQUARE ROOTS<\/strong> Find the square root(s).<br \/>\nQuestion 14.<br \/>\n\u221a625<\/p>\n<p>Answer:<br \/>\n25<\/p>\n<p>Explanation:<br \/>\n\u221a625<br \/>\n\u221a25\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of 625 is 25<\/p>\n<p>Question 15.<br \/>\n\u00b1 \u221a196<\/p>\n<p>Answer:<br \/>\n\u00b1 14<\/p>\n<p>Explanation:<br \/>\n\u00b1 \u221a196<br \/>\n\u221a14\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of 196 is 14<\/p>\n<p>Question 16.<br \/>\n&#8211; \u221a1600<\/p>\n<p>Answer:<br \/>\n&#8211; 40<\/p>\n<p>Explanation:<br \/>\n&#8211; \u221a1600<br \/>\n\u221a40\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of 1600 is 40<\/p>\n<p>Question 17.<br \/>\n\u00b1 \u221a2500<\/p>\n<p>Answer:<br \/>\n\u00b1 50<\/p>\n<p>Explanation:<br \/>\n\u00b1\u00a0\u221a2500<br \/>\n\u221a50\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of 2500 is 50<\/p>\n<p>Question 18.<br \/>\n\\(\\sqrt{\\frac{1}{16}}\\)<\/p>\n<p>Answer:<br \/>\n(1\/4)<\/p>\n<p>Explanation:<br \/>\n\u221a(1\/16)<br \/>\n\u221a(1\/4)\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of (1\/16) is (1\/4)<\/p>\n<p>Question 19.<br \/>\n\\(\\sqrt{\\frac{49}{576}}\\)<\/p>\n<p>Answer:<br \/>\n(7\/24)<\/p>\n<p>Explanation:<br \/>\n\u221a(49\/576)<br \/>\n\u221a(7\/24)\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of (49\/576) is (7\/24)<\/p>\n<p>Question 20.<br \/>\n\u00b1 \\(\\sqrt{\\frac{1}{961}}\\)<\/p>\n<p>Answer:<br \/>\n\u00b1(1\/31)<\/p>\n<p>Explanation:<br \/>\n\u221a(1\/961)<br \/>\n\u221a(1\/31)\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of (1\/961) is (1\/31)<\/p>\n<p>Question 21.<br \/>\n&#8211; \\(\\sqrt{\\frac{9}{100}}\\)<\/p>\n<p>Answer:<br \/>\n&#8211; (3\/10)<\/p>\n<p>Explanation:<br \/>\n\u221a(9\/100)<br \/>\n\u221a(3\/10)\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of (9\/100) is (3\/10)<\/p>\n<p>Question 22.<br \/>\n\u00b1 \u221a4.84<\/p>\n<p>Answer:<br \/>\n\u00b1 2.2<\/p>\n<p>Explanation:<br \/>\n\u221a4.84<br \/>\n\u221a2.2\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of 4.84 is 2.2<\/p>\n<p>Question 23.<br \/>\n\u221a7.29<\/p>\n<p>Answer:<br \/>\n2.7<\/p>\n<p>Explanation:<br \/>\n\u221a7.29<br \/>\n\u221a27\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of 7.29 is 2.7<\/p>\n<p>Question 24.<br \/>\n&#8211; \u221a361<\/p>\n<p>Answer:<br \/>\n&#8211; 19<\/p>\n<p>Explanation:<br \/>\n-\u221a361<br \/>\n\u221a19\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of\u00a0 361 is 19<\/p>\n<p>Question 25.<br \/>\n&#8211; \u221a2.25<\/p>\n<p>Answer:<br \/>\n&#8211; 1.5<\/p>\n<p>Explanation:<br \/>\n&#8211; \u221a2.25<br \/>\n\u221a15\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of\u00a0 2.25 is 1.5<\/p>\n<p>Question 26.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds \u00b1 \\(\\sqrt{\\frac{1}{4}}\\). Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 10\" width=\"168\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n\u00b1 (1\/2)<\/p>\n<p>Explanation:<br \/>\n\u00b1\u221a(1\/4)<br \/>\n\u221a(1\/2)\u00b2 therefore square and square root get canceled.<br \/>\nthe square root of\u00a0 (1\/4) is (1\/2)<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe area of a square patch of fabric is 2.25 square inches. What is the side length of the patch?<\/p>\n<p>Answer:<br \/>\n1.5 inch<\/p>\n<p>Explanation:<br \/>\nArea of a square patch of fabric is 2.25<br \/>\narea of a square is s\u00b2<br \/>\narea = 1.5 x 1.5<br \/>\nside = 1.5 inch<\/p>\n<p>Question 28.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThere are two square roots of 25. Why is there only one answer for the radius of the button?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 11\" width=\"140\" height=\"151\" \/><\/p>\n<p>Answer:<br \/>\nThe radius of the button = 5 mm<\/p>\n<p>Explanation:<br \/>\nGiven that the area of a circle = \u03c0r\u00b2<br \/>\n25\u03c0 = \u03c0r\u00b2<br \/>\nwhere \u03c0 get canceled on both sides.<br \/>\n25 = r\u00b2<br \/>\nr = 5<\/p>\n<p><strong>NUMBER SENSE<\/strong> Copy and complete the statement with &lt;, &gt;, or =.<br \/>\nQuestion 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 12\" width=\"86\" height=\"40\" \/><\/p>\n<p>Answer:<br \/>\n\u221a81 &gt; \u00a08<\/p>\n<p>Explanation:<br \/>\nsquare root\u00a0 of 81 = 9 x 9<br \/>\n9 is greater then\u00a0 8<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 13\" width=\"103\" height=\"44\" \/><\/p>\n<p>Answer:<br \/>\n0.5\u00a0 = \u221a0.25<\/p>\n<p>Explanation:<br \/>\nsquare root\u00a0 of 0.25 = 0.5 x 0.5<br \/>\n0.5 is equal to 0.5<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 14\" width=\"93\" height=\"44\" \/><\/p>\n<p>Answer:<br \/>\n(3\/2)\u00a0 &lt; \u221a(25\/4)<\/p>\n<p>Explanation:<br \/>\nsquare root\u00a0 of (25\/4) = (5\/2) x (5\/2)<br \/>\n(3\/2) is less than (5\/2)<br \/>\n(3\/2) = 1.5<br \/>\n(5\/2) = 3.5<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong> Evaluate the expression.<br \/>\nQuestion 32.<br \/>\n(\u221a9)<sup>2<\/sup> + 5<\/p>\n<p>Answer:<br \/>\n14<\/p>\n<p>Explanation:<br \/>\nsquare and square root get canceled.<br \/>\n9 + 5<br \/>\n14<\/p>\n<p>Question 33.<br \/>\n28 &#8211; (\u221a144)<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n-116<\/p>\n<p>Explanation:<br \/>\nsquare and square root get canceled.<br \/>\n28 &#8211; 144<br \/>\n-116<\/p>\n<p>Question 34.<br \/>\n3\u221a16 &#8211; 5<\/p>\n<p>Answer:<br \/>\n7<\/p>\n<p>Explanation:<br \/>\nthe square root of 16 is 4<br \/>\n16 = 4 x 4<br \/>\n3 x 4 &#8211; 5<br \/>\n12 &#8211; 5<br \/>\n7<\/p>\n<p>Question 35.<br \/>\n10 &#8211; 4\\(\\sqrt{\\frac{1}{16}}\\)<\/p>\n<p>Answer:<br \/>\n9<\/p>\n<p>Explanation:<br \/>\nthe square root of 16 is 4<br \/>\n16 = 4 x 4<br \/>\n10 &#8211; 4 (1\/4)<br \/>\n10 &#8211; 4 (0.25)<br \/>\n10 &#8211; 1<br \/>\n9<\/p>\n<p>Question 36.<br \/>\n\u221a6.76 + 5.4<\/p>\n<p>Answer:<br \/>\n12.56<\/p>\n<p>Explanation:<br \/>\nsquare and square root get canceled<br \/>\n6.76 + 5.4<br \/>\n12.16<\/p>\n<p>Question 37.<br \/>\n8\u221a8.41 + 1.8<\/p>\n<p>Answer:<br \/>\n25<\/p>\n<p>Explanation:<br \/>\nsquare and square root get canceled<br \/>\n8 x 8.41 + 1.8<br \/>\n67.28 + 1.8<br \/>\n69.08<\/p>\n<p>Question 38.<br \/>\n2(\\(\\sqrt{\\frac{80}{5}}\\) &#8211; 5)<\/p>\n<p>Answer:<br \/>\n3<\/p>\n<p>Explanation:<br \/>\nthe square root of 16 is 4 x 4<br \/>\n(80\/5) = 16<br \/>\n2 x 4 -5<br \/>\n8 &#8211; 5<br \/>\n3<\/p>\n<p>Question 39.<br \/>\n4(\\(\\sqrt{\\frac{147}{3}}\\) + 3<\/p>\n<p>Answer:<br \/>\n40<\/p>\n<p>Explanation:<br \/>\nthe square root of 49 is 7 x 7<br \/>\n(147\/3) = 49<br \/>\n4 x 7 + 3<br \/>\n37 + 3<br \/>\n40<\/p>\n<p>Question 40.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nWithout calculating, describe how the value of \\(\\sqrt{\\frac{1}{a}}\\) changes as a increases. Assume a &gt; 0.<br \/>\nAnswer:<br \/>\n0.5<\/p>\n<p>Explanation:<br \/>\nAssuming a &gt; 0<br \/>\na = 4<br \/>\nthe square root of 4 is 2<br \/>\n4 = 2 x 2<br \/>\n(1\/2) = 0.5<\/p>\n<p><strong>SOLVING EQUATIONS<\/strong> Solve the equation.<br \/>\nQuestion 41.<br \/>\nx<sup>2<\/sup> = 100<\/p>\n<p>Answer:<br \/>\nx = 10 , x = -10<\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> = 100<br \/>\nx\u00b2 = 10\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx = 10<\/p>\n<p>Question 42.<br \/>\n42 = d<sup>2<\/sup> &#8211; 22<\/p>\n<p>Answer:<br \/>\nd = 8 , d = 8<\/p>\n<p>Explanation:<br \/>\n42 = d<sup>2<\/sup> &#8211; 22<br \/>\nd\u00b2 = 42 + 22<br \/>\nd\u00b2 = 64<br \/>\nd\u00b2 = 8\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nd = 8<\/p>\n<p>Question 43.<br \/>\n4z<sup>2<\/sup> = 144<\/p>\n<p>Answer:<br \/>\nz = 6, z = -6<\/p>\n<p>Explanation:<br \/>\n4z<sup>2<\/sup> = 144<br \/>\nz\u00b2 = (144\/4)<br \/>\nz\u00b2 = 36<br \/>\nz\u00b2 = 6\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nz = 6<\/p>\n<p>Question 44.<br \/>\n\\(\\sqrt{\\frac{136}{9}}\\) = \\(\\frac{1}{3}\\) m<sup>2<\/sup> &#8211; 10<\/p>\n<p>Answer:<br \/>\nm = 4.8335, m = -4.8335<\/p>\n<p>Explanation:<br \/>\n(136\/9) = 45.33<br \/>\n(1\/3) = 0.333<br \/>\n0.3333 m<sup>2<\/sup> &#8211; 10<br \/>\nm<sup>2<\/sup>\u00a0 = 10 &#8211; 0.33<br \/>\nm<sup>2<\/sup> = 9.67<br \/>\nm = 4.835<\/p>\n<p>Question 45.<br \/>\n0.25r<sup>2<\/sup> = 49<\/p>\n<p>Answer:<br \/>\nr = 14, r = -14<\/p>\n<p>Explanation:<br \/>\n0.25r<sup>2<\/sup> = 49<br \/>\nr\u00b2 = (49\/0.25)<br \/>\nr\u00b2 = 196<br \/>\nr\u00b2 = 14\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nr = 14<\/p>\n<p>Question 46.<br \/>\n3h<sup>2<\/sup> = h<sup>2<\/sup> + 18<\/p>\n<p>Answer:<br \/>\nh = 3, h = -3<\/p>\n<p>Explanation:<br \/>\n3h<sup>2<\/sup> = h<sup>2<\/sup> + 18<br \/>\n3h\u00b2 &#8211; h\u00b2\u00a0 = 18<br \/>\n2h\u00b2\u00a0 = 18<br \/>\nh\u00b2\u00a0 = (18\/2)<br \/>\nh\u00b2\u00a0 = 9<br \/>\nh\u00b2\u00a0 = 3\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nh = 3<\/p>\n<p>Question 47.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend solves the equation 9x<sup>2<\/sup> = 36. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 15\" width=\"114\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nYes, my friend is correct.<\/p>\n<p>Explanation:<br \/>\n9x<sup>2<\/sup> = 36<br \/>\nx\u00b2 = (36\/9)<br \/>\nx\u00b2 = 4<br \/>\nx\u00b2 = 2\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx =2<\/p>\n<p>Question 48.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe period of a pendulum is the time the pendulum takes to complete one back-and-forth T swing. The period T (in seconds) can be modeled by the function T = 1.1\u221aL, where L is the length (in feet) of the pendulum. Estimate the length of a pendulum with a period of 1.65 seconds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 16\" width=\"271\" height=\"191\" \/><\/p>\n<p>Answer:<br \/>\nThe length of the pendulum with a period of 1.65 seconds = 0.50292 sec<\/p>\n<p>Explanation:<br \/>\nGiven that the period (in seconds) is 1.1<br \/>\n1.65 x 0.3048<br \/>\n1 feet = 0.3048 sec<br \/>\n0.50292<\/p>\n<p>Question 49.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe area of a sail is 40\\(\\frac{1}{2}\\) square feet. The base and the height of the sail are equal. What is the height of the sail?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 17\" width=\"161\" height=\"203\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the sail = 9 ft<\/p>\n<p>Explanation:<br \/>\nArea of triangle = (b h\/2)<br \/>\narea = 40 x (1\/2)<br \/>\n40 x 0.5 = 20<br \/>\nh = 9 , b = 4<br \/>\n(9 x 4\/2) = (36\/2)<br \/>\n18 = area<\/p>\n<p>Question 50.<br \/>\n<strong>REASONING<\/strong><br \/>\nIs the product of two perfect squares always a perfect square? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nYes, the product of two perfect squares always a perfect square.<\/p>\n<p>Explanation:<br \/>\nfor example, we take 9<br \/>\nthe square root of 9 = 3 x 3<br \/>\n3 is also a perfect square.<\/p>\n<p>Question 51.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe kinetic energy (in joules) of a falling apple is represented byK = \\(\\frac{v^{2}}{2}\\), where v is the speed of the apple (in meters per second). How fast is the apple traveling when the kinetic energy is 32 joules?<\/p>\n<p>Answer:<br \/>\nThe apple traveling when the kinetic energy is 32 joules = 8 meter per second.<\/p>\n<p>Explanation:<br \/>\nGiven that the apple is\u00a0 represented by k<br \/>\nk = 2 x 2<br \/>\nk = 4<br \/>\nalso given that 32 joules.<br \/>\n32 \/ 4 = 8 meter per sec.<\/p>\n<p>Question 52.<br \/>\n<strong>PRECISION<\/strong><br \/>\nThe areas of the two watch faces have a ratio of 16:25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 18\" width=\"203\" height=\"176\" \/><br \/>\na. What is the ratio of the radius of the smaller watch face to the radius of the larger watch face?<br \/>\nb. What is the radius of the larger watch face?<\/p>\n<p>Answer:<br \/>\na. The ratio of the radius of the smaller watch face to the radius of the larger watch face = 4: 5<br \/>\nb. the radius of the larger watch face = 25<\/p>\n<p>Explanation:<br \/>\na. square root of (16\/25) = (4\/5)<br \/>\nratio = 4: 5<br \/>\nb. the radius of the larger watch = 25<\/p>\n<p>Question 53.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe cost (in dollars) of making a square window with a side length of n inches is represented by C = \\(\\frac{n^{2}}{2}\\) + 175. A window costs $355. What is the side length (in feet) of the window? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe side length of the window = 2.5\u00a0 feet<\/p>\n<p>Explanation:<br \/>\nGiven that the window costs = 355$<br \/>\nthe side length of n inches is represented by c<br \/>\nthe side length of the window\u00a0 355 =\u00a0 n x n \/5+ 175<br \/>\nn = 30<br \/>\n(30\/12)<br \/>\n2.5 ft<br \/>\nQuestion 54.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAlbert Einstein\u2019s most famous equation is E = mc<sup>2<\/sup>, where E is the energy of an object (in joules), is the mass of the object (in kilograms), and c is the speed of light (in meters per second). A hydrogen atom has 15.066 \u00d7 10<sup>-7<\/sup> joule of energy and a mass of 1.674 \u00d7 10<sup>-27<\/sup> kilogram. What is the speed of light? Write your answer in scientific notation.<\/p>\n<p>Answer:<br \/>\nThe speed of the light =3 x 10\u00b2\u2070 meters per second.<\/p>\n<p>Explanation:<br \/>\nGiven that mass of the object = 1.674 x\u00a0 10<sup>-27<\/sup><br \/>\nenergy of the object = 15.066 x 10<sup>-7<\/sup><br \/>\nAlbert Einsteins equation = E = mc<sup>2<\/sup><br \/>\nwhere m = mass , e = energy, c = speed<br \/>\nc\u00b2 = (E\/M)<br \/>\nc\u00b2 = (15.066\/1.674)<br \/>\nc\u00b2 = 9 x 10\u00b2\u2070<br \/>\nc\u00b2 = 3\u00b2<br \/>\nc = 3 x 10\u00b2\u2070<\/p>\n<p>Question 55.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe area of the triangle is represented by the formula A = \\(\\sqrt{s(s-21)(s-17)(s-10)}\\), where s is equal to half the perimeter. What is the height of the triangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.1 19\" width=\"187\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nThe height of the triangle = 8 cm<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = 2 (A\/b)<br \/>\nwhere b = base A = area<br \/>\narea = 2 x 4<br \/>\narea = 8 cubic cm<\/p>\n<p>Question 56.<br \/>\n<strong>WRITING<\/strong><br \/>\nCan you find the square root of a negative number? Explain.<\/p>\n<p>Answer:<br \/>\nYes, we can find the square root of a negative number.<\/p>\n<p>Explanation:<br \/>\nThe square root of &#8211; 144 is &#8211; 12 x 12<br \/>\nthe square root of &#8211; ve number is also a + ve.<\/p>\n<p><strong>REASONING<\/strong> Without solving, determine the number of solutions of the equation.<br \/>\nQuestion 57.<br \/>\nx<sup>2<\/sup> = 1<\/p>\n<p>Answer:<br \/>\n2 solutions<br \/>\nx = 1, x = -1<\/p>\n<p>Explanation:<br \/>\nx\u00b2 = 1\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx = 1<\/p>\n<p>Question 58.<br \/>\nb<sup>2<\/sup> = &#8211; \\(\\sqrt{\\frac{1}{9}}\\)<\/p>\n<p>Answer:<br \/>\nb = -0.16, b = 0.16<\/p>\n<p>Explanation:<br \/>\nb<sup>2<\/sup> = &#8211; \\(\\sqrt{\\frac{1}{9}}\\)<br \/>\nsquare root of (1\/9) = (1\/3)<br \/>\nb\u00b2 = &#8211; (1\/3)<br \/>\nb\u00b2 = &#8211; 0.33<br \/>\nb = 0.16<\/p>\n<p>Question 59.<br \/>\nz = \u221a-144<\/p>\n<p>Answer:<br \/>\nz = 0<\/p>\n<p>Explanation:<br \/>\n\u221a-144 = \u221a(12 x 12 )\u00b2<br \/>\n\u221a-144 = 12<br \/>\nsquare and square root get cancelled.<br \/>\nz = -12<\/p>\n<h3><a id=\"Lesson_9.2_The_Pythagorean_Theorem\"><\/a>Lesson 9.2 The Pythagorean Theorem<\/h3>\n<p>Pythagoras was a Greek mathematician and philosopher who proved one of the most famous rules in mathematics. In mathematics, a rule is called a theorem. So, the rule that Pythagoras proved is called the Pythagorean Theorem.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 1\" width=\"148\" height=\"179\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Discovering the Pythagorean Theorem<br \/>\nWork with a partner.<\/p>\n<ul>\n<li>On grid paper,draw a right triangle with one horizontal side and one vertical side.<\/li>\n<li>Label the lengths of the two shorter sides a and b. Label the length of the longest side c.<\/li>\n<li>Draw three squares that each share a side with your triangle. Label the areas of the squares a<sup>2<\/sup>, b<sup>2<\/sup>, and c<sup>2<\/sup>.<\/li>\n<li>Cut out each square. Then make eight copies of the right triangle and cut them out.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 2\" width=\"520\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-2.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-2-300x120.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><br \/>\na. Arrange the figures to show how a<sup>2<\/sup> and b<sup>2<\/sup> relate to c<sup>2<\/sup>. Use an equation to represent this relationship.<br \/>\nb. Estimate the side length of your triangle. Then use the relationship in part(a) to find c. Compare the values.<\/p>\n<p>Answer:<br \/>\na. a\u00b2 + b\u00b2 = c\u00b2<br \/>\nb. 9 + 16 = 25<\/p>\n<p>Explanation:<br \/>\na. a\u00b2 + b\u00b2 = c\u00b2<br \/>\nb. we are estimating a = 3 , b = 4 , c =5<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n3\u00b2 + 4\u00b2 = 5\u00b2<br \/>\n9 + 16 = 25<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 3\" width=\"187\" height=\"136\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the length of the hypotenuse of the triangle.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-4.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 4\" width=\"194\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nLength = -6, 6<\/p>\n<p>Explanation:<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n15 &#8211; 8 = 6<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-5.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 5\" width=\"135\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nLength = 0.7<\/p>\n<p>Explanation:<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n0.4\u00b2 + 0.3\u00b2 =0.7\u00b2<br \/>\nlength = 0.7<\/p>\n<p><strong>Find the missing length of the triangle.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-6.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 6\" width=\"192\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nLength of the triangle = 8 , -8<\/p>\n<p>Explanation:<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n16\u00b2 -8 =8\u00b2<br \/>\nlength = 8yd<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-7.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 7\" width=\"177\" height=\"90\" \/><\/p>\n<p>Answer:<br \/>\nLength of the triangle = 0.8 m<\/p>\n<p>Explanation:<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n0.8\u00b2 + 9.6\u00b2 =10.4\u00b2<br \/>\nlength = 0.8 m<\/p>\n<p>Find x<br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-8.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 8\" width=\"171\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nx = 10 yd<\/p>\n<p>Explanation:<br \/>\na\u00b2 + b\u00b2 = x\u00b2<br \/>\n9\u00b2 + 1\u00b2 =10\u00b2<br \/>\nlength = 10 yd<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-9.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 9\" width=\"185\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nx = 15.4 ft<\/p>\n<p>Explanation:<br \/>\na\u00b2 + b\u00b2 = x\u00b2<br \/>\n6.6\u00b2 + 8.8\u00b2 =15.4\u00b2<br \/>\nlength = 15.4 ft<\/p>\n<p><strong>Find the distance between the points.<\/strong><br \/>\nQuestion 7.<br \/>\n(3, 6) and (7, 9)<\/p>\n<p>Answer:<br \/>\n3, 2<\/p>\n<p>Explanation:<br \/>\n(3,6) = (6- 3) = 3<br \/>\n(7 , 9) = (9 &#8211; 7) = 2<\/p>\n<p>Question 8.<br \/>\n(- 3, &#8211; 4) and (2, 8)<\/p>\n<p>Answer:<br \/>\n-7 , 6<\/p>\n<p>Explanation:<br \/>\n(-3 ,-4) = (-4- -3) = -7<br \/>\n(2 , 8) = (8 &#8211; 2) = 6<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>FINDING A MISSING LENGTH<\/strong> Find x.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-10.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 10\" width=\"157\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 1.6 ft<\/p>\n<p>Explanation:<br \/>\na\u00b2 + x\u00b2 = c\u00b2<br \/>\n2.4\u00b2 + 1.6\u00b2 =4\u00b2<br \/>\nlength = 1. 6 ft<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-11.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 11\" width=\"196\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 2.8 cm<\/p>\n<p>Explanation:<br \/>\na\u00b2 + x\u00b2 = c\u00b2<br \/>\n1.6\u00b2 + 1.2\u00b2 =2.8\u00b2<br \/>\nlength = 2.8 cm<\/p>\n<p>Question 11.<br \/>\n<strong>FINDING A DISTANCE<\/strong><br \/>\nFind the distance between (- 5, 2) and (7, &#8211; 7).<\/p>\n<p>Answer:<br \/>\n&#8211; 3 , 0<\/p>\n<p>Explanation:<br \/>\n(-5 ,2) = (-4 -2) = -3<br \/>\n(7 , -7) = (7 &#8211; 7) = 0<br \/>\n-3 , 0<\/p>\n<p>Question 12.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-12.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 12\" width=\"588\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-12.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-12-300x64.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Answer:<br \/>\nThe hypotenuse = c<br \/>\nlongest side = c<br \/>\nleg = c<br \/>\nopposite to right angle = c<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + x\u00b2 = c\u00b2<br \/>\nThe hypotenuse = c<br \/>\nlongest side = c<br \/>\nleg = c<br \/>\nopposite to right angle = c<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 13.<br \/>\nA zoo keeper knows that an escaped red panda is hiding somewhere in the triangular region shown. What is the area (in square miles) that the zoo keeper needs to search? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-13.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 13\" width=\"411\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-13.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-13-300x124.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Answer:<br \/>\nThe area that zoo keeper needs to search = 9.8 sq m<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n2.4 + 7.4 = 9.8 sq m<br \/>\nc\u00b2 = a\u00b2 + b\u00b2<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nObjects detected by radar are plotted in a coordinate plane where each unit represents 1 mile. The point (0, 0) represents the location of a shipyard. A cargo ship is traveling at a constant speed and in a constant direction parallel to the coastline. At9 A.M., the radar shows the cargo ship at(0, 15). At 10 A.M., the radar shows the cargo ship at(16, 15). How far is the cargo ship from the shipyard at 4 P.M.? Explain.<\/p>\n<p>Answer:<br \/>\nThe cargo ship from the shipyard at 4 p.m = (16, 0)<\/p>\n<p>Explanation:<br \/>\nGiven that cargo ship at (0, 15) 9 a.m<br \/>\ncargo ship at (16, 15) 10 a.m<br \/>\n(16 &#8211; 0) , (15 &#8211; 15)<br \/>\n(16, 0) at 4 p.m<\/p>\n<h3><a id=\"The_Pythagorean_Theorem_Homework_&amp;_Practice_9.2\"><\/a>The Pythagorean Theorem Homework &amp; Practice 9.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 1.<br \/>\n7z<sup>2<\/sup> = 252<\/p>\n<p>Answer:<br \/>\nz = 6<\/p>\n<p>Explanation:<br \/>\n7z<sup>2<\/sup> = 252<br \/>\nz\u00b2 = (252\/7)<br \/>\nz\u00b2 = 36<br \/>\nz\u00b2 = 6\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nz = 6<\/p>\n<p>Question 2.<br \/>\n0.75 q<sup>2<\/sup> = 108<\/p>\n<p>Answer:<br \/>\nq = 12<\/p>\n<p>Explanation:<br \/>\n0.75 q<sup>2<\/sup> = 108<br \/>\nq\u00b2 = (108\/0.75)<br \/>\nq\u00b2 = 144<br \/>\nq\u00b2 = 12\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nq = 12<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt{\\frac{1000}{10}}\\) = n<sup>2<\/sup> &#8211; 54<\/p>\n<p>Answer:<br \/>\nn = 8<\/p>\n<p>Explanation:<br \/>\n(1000\/10) = 100<br \/>\nsquare root of 100 = 10 x 10<br \/>\n10 = n\u00b2 &#8211; 54<br \/>\nn\u00b2 = 10 + 54<br \/>\nn\u00b2 = 64<br \/>\nn\u00b2 = 8\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nn = 8<\/p>\n<p>Question 4.<br \/>\nWhat is the solution of the system of linear equations y = 4x + 1 and 2x + y = 13?<br \/>\nA. (1, 5)<br \/>\nB. (5, 3)<br \/>\nC. (2, 9)<br \/>\nD. (9, 2)<\/p>\n<p>Answer:<br \/>\noption c is correct.<\/p>\n<p>Explanation:<br \/>\ny = 4x + 1, 2x + y = 13<br \/>\nif we consider x = 2 and y = 9 the values are equal.<br \/>\n9 = 4(2) + 1 , 2 (2) + 9 = 13<br \/>\n9 = 8 + 1, 4 + 9 = 13<br \/>\n9 = 9 , 13 = 13.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>USING GRID PAPER<\/strong> Find c. (See Exploration 1, p. 381.)<br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-14.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 14\" width=\"176\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\nThe value of c = 13<\/p>\n<p>Explanation:<br \/>\ngiven that grid paper<br \/>\na = 6 ( 6 boxes touching.)<br \/>\nb = 6 ( 8 boxes touching.)<br \/>\nc = 13 (13 boxes touching.)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-15.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 15\" width=\"256\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe value of c = 15<\/p>\n<p>Explanation:<br \/>\ngiven that grid paper<br \/>\na = 5 ( 5 boxes touching.)<br \/>\nb = 12 ( 12 boxes touching.)<br \/>\nc = 15 (15 boxes touching.)<\/p>\n<p><strong>FINDING A MISSING LENGTH<\/strong> Find the missing length of the triangle.<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-16.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 16\" width=\"130\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nThe missing length = 41km<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n20\u00b2 + 21\u00b2 =41\u00b2<br \/>\nlength = 41 km<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-17.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 17\" width=\"152\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-17.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-17-150x99.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 16.8 sq ft<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n7.2\u00b2 + 9.6\u00b2 =16.8\u00b2<br \/>\nlength = 16.8 sq ft<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-18.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 18\" width=\"106\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 5.0 sq in<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n5.0\u00b2 + 5.6\u00b2 =10.6\u00b2<br \/>\nlength = 10.6 sq in<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-19.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 19\" width=\"124\" height=\"87\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 6\u00a0 mm<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n9\u00b2 + 6\u00b2 =15\u00b2<br \/>\nlength = 6 mm<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-20.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 20\" width=\"146\" height=\"84\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 16\u00a0 cm<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n10\u00b2 + 16\u00b2 =26\u00b2<br \/>\nlength = 16 cm<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-21.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 21\" width=\"160\" height=\"80\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 5.0 yd<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n5.0\u00b2 + 1.1\u00b2 = 6.1\u00b2<br \/>\nlength = 5.0 yd<\/p>\n<p>Question 13.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the missing length of the triangle. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-22.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 22\" width=\"288\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\nNo my friend is not correct.<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n7\u00b2 + 18\u00b2 = 25\u00b2<br \/>\nlength = 18 ft<\/p>\n<p><strong>FINDING LENGTHS OF THREE-DIMENSIONAL FIGURES<\/strong> Find x.<br \/>\nQuestion 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-23.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 23\" width=\"138\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 14 ft<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n10\u00b2 + 14\u00b2 = 24\u00b2<br \/>\nlength = 14 ft<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-24.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 24\" width=\"215\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 50 in<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n14\u00b2 + 48\u00b2 = 50\u00b2<br \/>\nlength = 50 in<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-25.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 25\" width=\"167\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 0.6 m<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n0.6\u00b2 + 0.9\u00b2 = 1.5\u00b2<br \/>\nlength = 0.6 m<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-26.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 26\" width=\"146\" height=\"147\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 6 cm<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n4.5\u00b2 + 2.5\u00b2 = 6\u00b2<br \/>\nlength = 6 cm<\/p>\n<p><strong>FINDING DISTANCES IN THE COORDINATE PLANE<\/strong> Find the distance between the points.<br \/>\nQuestion 18.<br \/>\n(0, 0), (9, 12)<\/p>\n<p>Answer:<br \/>\n(9,12)<\/p>\n<p>Explanation:<br \/>\n(0, 0), (9, 12)<br \/>\n(9-0) = 9<br \/>\n(12 &#8211; 0) = 12<\/p>\n<p>Question 19.<br \/>\n(1, 2), (- 3, 5)<\/p>\n<p>Answer:<br \/>\n5 units<br \/>\nExplanation:<br \/>\n(1, 2), (-3, 5)<br \/>\n(-3-1) = -4<br \/>\n(5- 2) = 5<\/p>\n<p>Question 20.<br \/>\n(\u201418, 9), (22, 0)<\/p>\n<p>Answer:<br \/>\n(4,9)<\/p>\n<p>Explanation:<br \/>\n(\u201418, 9), (22, 0)<br \/>\n(22-18) = 4<br \/>\n(9- 0) = 9<\/p>\n<p>Question 21.<br \/>\n(- 7, &#8211; 2), (13, &#8211; 23)<\/p>\n<p>Answer:<br \/>\n29 units<\/p>\n<p>Explanation:<br \/>\n(- 7, &#8211; 2), (13, &#8211; 23)<br \/>\n(13-7) = 6<br \/>\n(-23- 2) = -25<\/p>\n<p>Question 22.<br \/>\n(15, &#8211; 17), (- 20, &#8211; 5)<\/p>\n<p>Answer:<br \/>\n(-35, -22)<\/p>\n<p>Explanation:<br \/>\n(15, &#8211; 17), (- 20, &#8211; 5)<br \/>\n(-20-15) = -35<br \/>\n(-5- 17) = -22<\/p>\n<p>Question 23.<br \/>\n(- 13, &#8211; 3.5), (17, 2)<\/p>\n<p>Answer:<br \/>\n(30, 18.5)<\/p>\n<p>Explanation:<br \/>\n(- 13, &#8211; 3.5), (17, 2)<br \/>\n(17+13) = 30<br \/>\n(15+ 3.5) = 18.5<\/p>\n<p><strong>FINDING A MISSING LENGTH<\/strong> Find x.<br \/>\nQuestion 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-27.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 27\" width=\"175\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 8 cm<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n8\u00b2 + 12\u00b2 = 20\u00b2<br \/>\nlength = 8 cm<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-28.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 28\" width=\"223\" height=\"96\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 37 mm<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n13\u00b2 + 22\u00b2 = 37\u00b2<br \/>\nlength = 37 mm<\/p>\n<p>Question 26.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe figure shows the location of a golf ball after a tee shot. How many feet from the hole is the ball?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-29.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 29\" width=\"196\" height=\"295\" \/><\/p>\n<p>Answer:<br \/>\nThe ball from the hole = 540 feet<\/p>\n<p>Explanation:<br \/>\nGiven that the hole and\u00a0 ball is<br \/>\n180 x 3<br \/>\n540 feet<br \/>\n1 yd = 3 ft<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA tennis player asks the referee a question. The sound of the player\u2019s voice travels 30 feet. Can the referee hear the question? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-30.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 30\" width=\"403\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-30.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-30-300x127.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Answer:<br \/>\nYes, the referee hears the voice.<\/p>\n<p>Explanation:<br \/>\nIn the question given that the sound of the player&#8217;s voice travels 30 feet.<br \/>\nin the figure given that 24 feet.<br \/>\nso the referee can hear the voice.<\/p>\n<p>Question 28.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou are cutting a rectangular piece of fabric in half along a diagonal. The fabric measures 28 inches wide and 1\\(\\frac{1}{4}\\) yards long. What is the length (in inches) of the diagonal?<\/p>\n<p>Answer:<br \/>\nThe length of the diagonal = 28.25 in<\/p>\n<p>Explanation:<br \/>\nGiven that the fabric wides = 28 inches.<br \/>\n(1\/4) = 0.25 in<br \/>\nThe length of the diagonal\u00a0 = 28 x 0.25<br \/>\n28.25 in<\/p>\n<p>Question 29.<br \/>\n<strong>PROJECT<\/strong><br \/>\nMeasure the length, width, and height of a rectangular room. Use the Pythagorean Theorem to find the distance from B to C and the distance from A to B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-31.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 31\" width=\"187\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\na\u00b2 + b\u00b2\u00a0 = c\u00b2<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\nlength + width = height<\/p>\n<p>Question 30.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe legs of a right triangle have lengths of 28 meters and 21 meters. The hypotenuse has a length of 5x meters. What is the value of x?<\/p>\n<p>Answer:<br \/>\nThe value of x = 9.8 meters.<\/p>\n<p>Explanation:<br \/>\nGiven that the right triangle has length\u00a0 = 28 meters and 21 meters.<br \/>\nthe hypotenuse = 5x<br \/>\n28 + 21 = 5x<br \/>\n49 = 5x<br \/>\nx = (49\/5)<br \/>\nx = 9.8 meters.<\/p>\n<p>Question 31.<br \/>\n<strong>PRECISION<\/strong><br \/>\nYou and a friend stand back-to-back. You run 20 feet forward, then 15 feet to your right. At the same time, your friend runs 16 feet forward, then 12 feet to her right. She stops and hits you with a snowball.<br \/>\na. Draw the situation in a coordinate plane.<br \/>\nb. How far does your friend throw the snowball?<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe coordinate plane shows dig sites for archaeological research. Each unit on the grid represents 1 square foot. What is the distance from Site A to Site C?<\/p>\n<p>Answer:<br \/>\n7 square feet.<\/p>\n<p>Explanation:<br \/>\nGiven that each grid represents 1 sq feet.<br \/>\nin the below figure shows that the distance.<br \/>\ndistance from site A to site C is 7 sq ft.<br \/>\nthe boxes 7 are touching the edges of the site A to B<\/p>\n<p>Question 33.<br \/>\n<strong>PRECISION<\/strong><br \/>\nA box has a length of 30 inches, a width of 40 inches, and a height of 120 inches. Can a cylindrical rod with a length of 342.9 centimeters fit in the box? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-32.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 32\" width=\"152\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\nNo, the cylindrical rod with a length of 135 cm will fit in the box.<\/p>\n<p>Explanation:<br \/>\nGiven that the box has a length = 30 in<br \/>\nwidth = 40 in<br \/>\nheight = 120 in<br \/>\narea = l x w x h<br \/>\narea = 30 x 40 x 120<br \/>\narea = 1,44,000 cm<\/p>\n<p>Question 34.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA green roof is like a traditional roof but covered with plants. Plants used for a green roof cost $0.75 per square foot. The roof at the right is 40 feet long. How much does it cost to cover both sides of the roof? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-33.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 33\" width=\"252\" height=\"153\" \/><\/p>\n<p>Answer:<br \/>\nThe cost to cover both sides of the roof = 60 sq ft<\/p>\n<p>Explanation:<br \/>\nGiven that the plants used for a green roof cost = $0.75 sq ft.<br \/>\nthe roof at the right = 40 ft long<br \/>\nthe roof at both sides = 40 + 40 =80<br \/>\n1 sq feet = 0.75 $<br \/>\n80 x $0.75 = 60 sq ft<\/p>\n<p>Question 35.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA triangle has coordinates A(2, 1), B(2, 4), and C(5, 1). Write an expression for the length of \\(\\overline{B C}\\). Use a calculator to find the length of \\(\\overline{B C}\\) to the nearest hundredth.<\/p>\n<p>Answer:<br \/>\n4.24 units<\/p>\n<p>Question 36.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWrite an equation for the distance d between the points (x<sub>1<\/sub>, y<sub>1<\/sub>) and (x<sub>2<\/sub>, y<sub>2<\/sub>). Explain how you found the equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.2-34.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.2 34\" width=\"142\" height=\"143\" \/><\/p>\n<p>Answer:<br \/>\nx1 + y1 = x2 + y2<\/p>\n<p>Explanation:<br \/>\nGiven that the points (x1, y1) and (x2 , y2)<br \/>\nthe equation is<br \/>\nx1 + y1 = x2 + y2<\/p>\n<h3><a id=\"Lesson_9.3_Finding_Cube_Roots2\"><\/a>Lesson 9.3 Finding Cube Roots<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding Edge Lengths<br \/>\nWork with a partner. Find the edge length of each cube. Explain your method.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 1\" width=\"645\" height=\"356\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-1.png 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-1-300x166.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><\/p>\n<p>Answer:<br \/>\na. 2 cm<br \/>\nb. 3 ft<br \/>\nc. 5m<br \/>\nd. 7 in<br \/>\ne. 0.1 cm<br \/>\nf. 0.5 yd<\/p>\n<p>Explanation:<br \/>\na. volume = 8 = 2 x 2 x 2<br \/>\nb. 27 = 3 x 3 x 3<br \/>\nc. 125 = 5 x 5 x 5<br \/>\nd. 343 = 7 x 7 x 7<br \/>\ne. 0.001 = 0.1 x 0.1 x 0.1<br \/>\nf. (1\/8) = 0.5 x 0.5 x 0.5<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding Solutions of Equations<br \/>\nWork with a partner. Use mental math to solve each equation. How many solutions are there for each equation? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 2\" width=\"385\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-2.png 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-2-300x105.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<p>Answer:<br \/>\nx = -3<br \/>\nx = -2<br \/>\nx = -1<br \/>\nx = 1<br \/>\nx = 2<br \/>\nx = 3<\/p>\n<p>Explanation:<br \/>\nx\u00b3 = -27<br \/>\nx\u00b3 = -3\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx = -3<br \/>\nx\u00b3 = -8<br \/>\nx\u00b3 = -2\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx = -2<br \/>\nx\u00b3 = -1<br \/>\nx\u00b3 = -1\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx = -1<br \/>\nx\u00b3 = 27<br \/>\nx\u00b3 = 3\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx = 3<br \/>\nx\u00b3 = 8<br \/>\nx\u00b3 = 2\u00b3<br \/>\nwhen powers are equal exponents must be equal<br \/>\nx = 2<br \/>\nx\u00b3 = 1<br \/>\nx\u00b3 =1\u00b3<br \/>\nwhen powers are equal exponents must be equal<br \/>\nx = 1<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 3\" width=\"185\" height=\"86\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the cube root.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\sqrt [ 3 ]{ 1 } \\)<\/p>\n<p>Answer:<br \/>\n1<\/p>\n<p>Explanation:<br \/>\ncube root of 1 is\u00a0 1<br \/>\n3\u221a1 = 1<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt [ 3 ]{ -343 } \\)<\/p>\n<p>Answer:<br \/>\n-7<\/p>\n<p>Explanation:<br \/>\ncube root of -343 is\u00a0 -7<br \/>\n3\u221a -343= 7 x 7 x 7<br \/>\n(-343)\u00b3 = 7\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-343 = 7<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt[3]{-\\frac{27}{1000}}\\)<\/p>\n<p>Answer:<br \/>\n(-3\/10)<\/p>\n<p>Explanation:<br \/>\ncube root of -27 is\u00a0 -3<br \/>\n3\u221a -27= 3 x 3 x 3<br \/>\n(-27)\u00b3 = 3\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-27 = 3<br \/>\ncube root of -1000 is\u00a0 -10<br \/>\n3\u221a -1000= 10 x 10 x 10<br \/>\n(-1000)\u00b3 = 10\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-1000= 10<\/p>\n<p><strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 4.<br \/>\n18 &#8211; 4 \\(\\sqrt [ 3 ]{ 8 } \\)<\/p>\n<p>Answer:<br \/>\n10<\/p>\n<p>Explanation:<br \/>\ncube root of 8 is\u00a0 2<br \/>\n3\u221a 8 = 2 x 2 x 2<br \/>\n(8)\u00b3 = 2\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n8= 2<br \/>\n18 &#8211; 4 (2)<br \/>\n18 &#8211; 8<br \/>\n10<\/p>\n<p>Question 5.<br \/>\n(\\(\\sqrt[3]{-64})^{3}\\)) + 43<\/p>\n<p>Answer:<br \/>\n44.333<\/p>\n<p>Explanation:<br \/>\ncube root of -64 is\u00a0 -4<br \/>\n3\u221a -64 = 4 x 4 x 4<br \/>\n(-64)\u00b3 = 4\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-64= 4<br \/>\n1.333 + 43<br \/>\n44.333<\/p>\n<p>Question 6.<br \/>\n5\\(\\sqrt [ 3 ]{ 512 } \\) &#8211; 19<\/p>\n<p>Answer:<br \/>\n21<\/p>\n<p>Explanation:<br \/>\ncube root of 512 is\u00a0 8<br \/>\n3\u221a512 = 8 x 8 x 8<br \/>\n(512)\u00b3 = 8\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n512= 8<br \/>\n5 x 8 -19<br \/>\n40 &#8211; 19<br \/>\n21<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 7.<br \/>\nz<sup>3<\/sup> = &#8211; 1000<\/p>\n<p>Answer:<br \/>\nz = -10<\/p>\n<p>Explanation:<br \/>\ncube root of -1000 is\u00a0 -10<br \/>\n3\u221a-1000 = 10 x 10 x 10<br \/>\nz<sup>3<\/sup> \u00a0= 10\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nz= -10<\/p>\n<p>Question 8.<br \/>\n3b<sup>3<\/sup> = 1029<\/p>\n<p>Answer:<br \/>\nb = 7<\/p>\n<p>Explanation:<br \/>\n3b<sup>3<\/sup> = 1029<br \/>\nb\u00b3 = (1029\/3)<br \/>\nb\u00b3 = 343<br \/>\ncube root of 343 is\u00a0 7<br \/>\n3\u221a343 = 7 x 7 x 7<br \/>\nb\u00b3\u00a0 = 7\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nb = 7<\/p>\n<p>Question 9.<br \/>\n33 = &#8211; \\(\\frac{1}{5}\\) m<sup>3<\/sup> + 8<\/p>\n<p>Answer:<br \/>\nm\u00b3 = 25.8<\/p>\n<p>Explanation:<br \/>\n33 = &#8211; 0.2 m\u00b3\u00a0 + 8<br \/>\nm\u00b3\u00a0 = 33+0.2 -8<br \/>\nm\u00b3\u00a0 = 25.8<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>FINDING CUBE ROOTS<\/strong> Find the cube root.<br \/>\nQuestion 10.<br \/>\n\\(\\sqrt [ 3 ]{ 64 } \\)<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\ncube root of 64 is\u00a0 4<br \/>\n3\u221a64 = 4 x 4 x 4<br \/>\n64\u00b3 = 4\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n64 = 4<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt [ 3 ]{ -216 } \\)<\/p>\n<p>Answer:<br \/>\n-6<\/p>\n<p>Explanation:<br \/>\ncube root of -216 is\u00a0 -6<br \/>\n3\u221a-216 = 6 x 6 x 6<br \/>\n216\u00b3 = 6\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n216 = 6<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt[3]{-\\frac{343}{100}}\\)<\/p>\n<p>Answer:<br \/>\n&#8211; 7<\/p>\n<p>Explanation:<br \/>\ncube root of\u00a0 -343 is\u00a0 -7<br \/>\n3\u221a-343 = 7 x 7 x 7<br \/>\n-343\u00b3 = 7\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-343 = 7<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong> Evaluate the expression.<br \/>\nQuestion 13.<br \/>\n\\((\\sqrt[3]{-27})^{3}\\) + 61<\/p>\n<p>Answer:<br \/>\n52<\/p>\n<p>Explanation:<br \/>\ncube root of\u00a0 -27 is\u00a0 -3<br \/>\n3\u221a-27 = 3 x 3 x 3<br \/>\n-27\u00b3 = 3\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-27 = -3<br \/>\n-3 x 3 + 61<br \/>\n-9 + 61<br \/>\n52<\/p>\n<p>Question 14.<br \/>\n15 + 3\\(\\sqrt[3]{125}\\)<\/p>\n<p>Answer:<br \/>\n30<\/p>\n<p>Explanation:<br \/>\ncube root of\u00a0 125 is\u00a0 5<br \/>\n3\u221a125 = 5 x 5 x 5<br \/>\n125\u00b3 = 5\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n125 = 5<br \/>\n15 + 3 (5)<br \/>\n15 + 15<br \/>\n30<\/p>\n<p>Question 15.<br \/>\nz\\(\\sqrt[3]{-729}\\) &#8211; 5<\/p>\n<p>Answer:<br \/>\n-14<\/p>\n<p>Explanation:<br \/>\ncube root of\u00a0 -729 is\u00a0 -9<br \/>\n3\u221a-729 = 9 x 9 x 9<br \/>\n729\u00b3 = 9\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n729 = 9<br \/>\n-9 -5 = -14<\/p>\n<p><strong>SOLVING EQUATIONS<\/strong> Solve the equation.<br \/>\nQuestion 16.<br \/>\nd<sup>3<\/sup> = 512<\/p>\n<p>Answer:<br \/>\nd = 8<\/p>\n<p>Explanation:<br \/>\ncube root of\u00a0 512 is\u00a0 8<br \/>\n3\u221a512 = 8 x 8 x 8<br \/>\n512\u00b3 = 8\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nd\u00b3 = 8\u00b3<br \/>\nd = 8<\/p>\n<p>Question 17.<br \/>\nw<sup>3<\/sup> &#8211; 12 = &#8211; 76<\/p>\n<p>Answer:<br \/>\nw = -4<\/p>\n<p>Explanation:<br \/>\nw<sup>3<\/sup> &#8211; 12 = &#8211; 76<br \/>\nw\u00b3 = -76 + 12<br \/>\nw\u00b3 = -64<br \/>\ncube root of\u00a0 -64 is\u00a0 -4<br \/>\n3\u221a-64 = 4 x 4 x 4<br \/>\nw\u00b3 = 4\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nw = 4<\/p>\n<p>Question 18.<br \/>\n&#8211; \\(\\frac{1}{3}\\)m<sup>3<\/sup> + 13 = 4<\/p>\n<p>Answer:<br \/>\n-8.67<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 19.<br \/>\nYou have 275 square inches of wrapping paper. Do you have enough wrapping paper to wrap the gift box shown? Explain.<\/p>\n<p>Answer:<br \/>\nYes i have enough wrapping paper to wrap the gift box.<\/p>\n<p>Explanation:<br \/>\nGiven that 275 sq in of wrapping paper.<br \/>\n6.5 x 6.5 x 6.5 = 274.6<br \/>\n275 sq in<\/p>\n<p>Question 20.<br \/>\nA cube-shaped end table has a volume of 16,000 cubic centimeters. Does the end table fit in the corner shown? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 4\" width=\"134\" height=\"153\" \/><br \/>\nAnswer:<br \/>\nNo the end table does not fit in the corner.<\/p>\n<p>Explanation:<br \/>\nvolume = 343<br \/>\n343\u00b3 = 7\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n343 = 7<\/p>\n<p>Question 21.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-5.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 5\" width=\"193\" height=\"199\" \/><br \/>\nThe relationship between the volumes and the lengths of two cereal boxes is represented by<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 6\" width=\"242\" height=\"53\" \/><br \/>\nBox A has a volume of 192 cubic inches and a length of 8 inches. Box B has a volume of 375 cubic inches. What is the length of Box B? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe length of the box B = 1.6 inches.<\/p>\n<p>Explanation:<br \/>\n(v of A\/ v of B ) = ( l of A \/ l of B) \u00b3<br \/>\nB\u00b3 = (192\/375) x 8<br \/>\nb\u00b3 = 0.512 x 8<br \/>\nb\u00b3 = 4.096<br \/>\nb \u00b3 = 1.6\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nb = 1.6<\/p>\n<h3><a id=\"Finding_Cube_Roots_Homework_&amp;_Practice_9.3\"><\/a>Finding Cube Roots Homework &amp; Practice 9.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the missing length of the triangle.<\/strong><br \/>\nQuestion 1<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 7\" width=\"137\" height=\"95\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 40 m<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n24\u00b2 + 32\u00b2 = 40\u00b2<br \/>\n576 + 1024 = 1600<br \/>\n1600 = 1600<br \/>\nlength = 56m<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 8\" width=\"200\" height=\"87\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 10 ft<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n7.8\u00b2 + 10\u00b2 = 17.8\u00b2<br \/>\nlength = 10 ft<\/p>\n<p>Question 3.<br \/>\nWhich linear function is shown by the table?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-9.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 9\" width=\"491\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-9.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-9-300x52.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\nAnswer:<br \/>\noption C is correct.<\/p>\n<p>Explanation:<br \/>\ny = 3x + 1<br \/>\nx = 1, y = 4<br \/>\n4 = 3(1) + 1<br \/>\ny= 4<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>FINDING EDGE LENGTHS<\/strong> Find the edge length s of the cube. (See Exploration 1, p. 389.)<br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-10.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 10\" width=\"147\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\nThe edge length of the cube = 6<\/p>\n<p>Explanation:<br \/>\ncube root of\u00a0 216 is\u00a0 6<br \/>\n3\u221a216 = 6 x 6 x 6<br \/>\n216\u00b3 = 6\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\ns\u00b3 = 6\u00b3<br \/>\ns = 6<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-11.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 11\" width=\"150\" height=\"162\" \/><\/p>\n<p>Answer:<br \/>\nThe edge length of the cube = (1\/3) ft<\/p>\n<p>Explanation:<br \/>\ncube root of\u00a0 (1\/27) is\u00a0 (1\/3)<br \/>\n3\u221a(1\/27) = (1\/3)x (1\/3)\u00a0 x (1\/3)<br \/>\n(1\/27)\u00b3 = (1\/3)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\ns\u00b3 = (1\/3)\u00b3<br \/>\ns = (1\/3)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-12.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 12\" width=\"156\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nThe edge length of the cube = 0.4<\/p>\n<p>Explanation:<br \/>\ncube root of\u00a0 0.064 is\u00a0 0.4<br \/>\n3\u221a0.064 = 0.4 x 0.4\u00a0 x 0.4<br \/>\n0.064\u00b3 = 0.4\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\ns\u00b3 = 0.4\u00b3<br \/>\ns = 0.4<\/p>\n<p><strong>FINDING CUBE ROOTS<\/strong> Find the cube root.<br \/>\nQuestion 7.<br \/>\n\\(\\sqrt [ 3 ]{ 729 } \\)<\/p>\n<p>Answer:<br \/>\n9<\/p>\n<p>Explanation:<br \/>\ncube root of 729 is 9<br \/>\n3\u221a729 = 9 x 9 x 9<br \/>\n729\u00b3 = 9\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n729 = 9<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 3 ]{ -125 } \\)<\/p>\n<p>Answer:<br \/>\n-5<\/p>\n<p>Explanation:<br \/>\ncube root of -125 is -5<br \/>\n3\u221a-125 = 5 x 5 x 5<br \/>\n-125\u00b3 = -5\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n125 = -5<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 3 ]{ -1000} \\)<\/p>\n<p>Answer:<br \/>\n-10<\/p>\n<p>Explanation:<br \/>\ncube root of -1000 is -10<br \/>\n3\u221a-1000 = 10 x 10 x 10<br \/>\n-1000\u00b3 = -10\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-1000 = -10<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt [ 3 ]{ 1728 } \\)<\/p>\n<p>Answer:<br \/>\n12<\/p>\n<p>Explanation:<br \/>\ncube root of 1728 is 12<br \/>\n3\u221a1728 = 12 x 12 x 12<br \/>\n1728\u00b3 = 12\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n1728 = 12<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt[3]{-\\frac{1}{512}}\\)<\/p>\n<p>Answer:<br \/>\n(-1\/6)<\/p>\n<p>Explanation:<br \/>\ncube root of &#8211; 512 is -(1\/6)<br \/>\n3\u221a-512 = (1\/6) x (1\/6) x (1\/6)<br \/>\n-512\u00b3 = -(1\/6)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-512 = (-1\/6)<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt[3]{\\frac{343}{64}}\\)<\/p>\n<p>Answer:<br \/>\n(7\/4)<\/p>\n<p>Explanation:<br \/>\ncube root of (343\/64) is (7\/4)<br \/>\n3\u221a343 = (7\/4) x (7\/4) x (7\/4)<br \/>\n343\u00b3 = (7\/4)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n343 = (7\/4)<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong> Evaluate the expression.<br \/>\nQuestion 13.<\/p>\n<p>18 &#8211; (\\(\\sqrt [ 3 ]{ 27 }\\))<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\n-9<\/p>\n<p>Explanation:<br \/>\n3\u221a27\u00b3 = 27<br \/>\nwhere cube and cube root get cancelled.<br \/>\n18 &#8211; 27<br \/>\n-9<\/p>\n<p>Question 14.<br \/>\n\\(\\left(\\sqrt[3]{-\\frac{1}{8}}\\right)^{3}\\) + 3\\(\\frac{3}{4}\\)<\/p>\n<p>Answer:<br \/>\n1.75<\/p>\n<p>Explanation:<br \/>\ncube root of (1\/18) is -(1\/2)<br \/>\n3\u221a(1\/18) = (1\/2) x (1\/2) x (1\/2)<br \/>\n(1\/18)\u00b3 = (1\/2)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n(1\/18) =- (1\/2)<br \/>\n-(1\/2) + 3(3\/4)<br \/>\n&#8211; 0.5 + 3 (0.75)<br \/>\n-0.5 + 2.25<br \/>\n1.75<\/p>\n<p>Question 15.<br \/>\n5\\(\\sqrt[3]{729}\\) &#8211; 24<\/p>\n<p>Answer:<br \/>\n21<\/p>\n<p>Explanation:<br \/>\ncube root of (729) is (9)<br \/>\n3\u221a729 = (9) x (9) x (9)<br \/>\n729\u00b3 = (9)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n729 = 9<br \/>\n5 x 9 -24<br \/>\n45 &#8211; 24<br \/>\n21<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{1}{4}-2 \\sqrt[3]{\\frac{1}{216}}\\)<\/p>\n<p>Answer:<br \/>\n-11.75<\/p>\n<p>Explanation:<br \/>\ncube root of (216) is (6)<br \/>\n3\u221a216 = (6) x (6) x (6)<br \/>\n216\u00b3 = (6)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n216 = 6<br \/>\n(1\/4) -2 (6)<br \/>\n(1\/4) &#8211; 12<br \/>\n0.25 &#8211; 12<br \/>\n-11.75<\/p>\n<p>Question 17.<br \/>\n54 + \\(\\sqrt[3]{-4096}\\)<\/p>\n<p>Answer:<br \/>\n38<\/p>\n<p>Explanation:<br \/>\ncube root of (-4096) is (-16)<br \/>\n3\u221a-4096 = (-16) x (-16) x (-16)<br \/>\n-4096\u00b3 = (-16)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n4096 = -16<br \/>\n54 +(-16)<br \/>\n54 &#8211; 16<br \/>\n38<\/p>\n<p>Question 18.<br \/>\n4\\(\\sqrt[3]{8000}\\) &#8211; 6<\/p>\n<p>Answer:<br \/>\n166<\/p>\n<p>Explanation:<br \/>\ncube root of (8000) is (43)<br \/>\n3\u221a8000 = (43) x (43) x (43)<br \/>\n8000\u00b3 = (43)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n8000 = 43<br \/>\n4 x 43 -6<br \/>\n172 &#8211; 6<br \/>\n166<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong> Evaluate the expression for the given value of the variable.<br \/>\nQuestion 19.<br \/>\n\\(\\sqrt[3]{\\frac{n}{4}}+\\frac{n}{10}\\), n = 500<\/p>\n<p>Answer:<br \/>\n55<\/p>\n<p>Explanation:<br \/>\n(500\/4) = 125<br \/>\n(500\/10) = 50<br \/>\ncube root of (125) is (5)<br \/>\n3\u221a125 = (5) x (5) x (5)<br \/>\n125\u00b3 = (5)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n125 = 5<br \/>\n5 + 50<br \/>\n55<\/p>\n<p>Question 20.<br \/>\n\\(\\sqrt[3]{6 w}\\) &#8211; w, w = 288<\/p>\n<p>Answer:<br \/>\n276<\/p>\n<p>Explanation:<br \/>\nw = 288 given<br \/>\n6 x 288 = 1728<\/p>\n<p>Question 21.<br \/>\n2d + \\(\\sqrt[3]{-45 d}\\), d = 75<\/p>\n<p>Answer:<br \/>\n165<\/p>\n<p>Explanation:<br \/>\nd = 75 given<br \/>\n-45 x 75 = -3375<br \/>\ncube root of (-3375) is (-15)<br \/>\n3\u221a-3375 = (-15) x (15) x (15)<br \/>\n(-3375)\u00b3 = (-15)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n3375 = 15<br \/>\n2x 75 + 15<br \/>\n150 +15<br \/>\n165<\/p>\n<p><strong>SOLVING EQUATIONS<\/strong> Solve the equation.<br \/>\nQuestion 22.<br \/>\nx<sup>3<\/sup> = 8<\/p>\n<p>Answer:<br \/>\nx = 2<\/p>\n<p>Explanation:<br \/>\nx<sup>\u00b3<\/sup>= 8<br \/>\nx\u00b3 = 2\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx = 2<\/p>\n<p>Question 23.<br \/>\nt<sup>3<\/sup> = &#8211; 343<\/p>\n<p>Answer:<br \/>\nt = &#8211; 7<\/p>\n<p>Explanation:<br \/>\nt\u00b3 = -343<br \/>\nt\u00b3 = -7\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nt = -7<\/p>\n<p>Question 24.<br \/>\n&#8211; 75 = y<sup>3<\/sup> + 50<\/p>\n<p>Answer:<br \/>\ny = -5<\/p>\n<p>Explanation:<br \/>\n&#8211; 75 = y<sup>3<\/sup> + 50<br \/>\ny\u00b3 = -75 &#8211; 50<br \/>\ny\u00b3 = -125<\/p>\n<p>y\u00b3 = -5\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\ny = -5<\/p>\n<p>Question 25.<br \/>\n&#8211; \\(\\frac{1}{2}\\)z<sup>3<\/sup> = &#8211; 108<\/p>\n<p>Answer:<br \/>\nz = 6<\/p>\n<p>Explanation:<br \/>\n-(1\/2)z\u00b3 = -108<br \/>\n(1\/2) = 0.5<br \/>\n-0.5z\u00b3 = -108<br \/>\nz\u00b3 = (-108 \/-0.5)<br \/>\nz\u00b3 = 216<br \/>\nz\u00b3 = 6\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nz = 6<\/p>\n<p>Question 26.<br \/>\n2h<sup>3<\/sup> &#8211; 11 = 43<\/p>\n<p>Answer:<br \/>\nh = 17<\/p>\n<p>Explanation:<br \/>\n2h<sup>3<\/sup> &#8211; 11 = 43<br \/>\n2h\u00b3 = 43 + 11<br \/>\n2h\u00b3 = 54<br \/>\nh\u00b3 = (54\/2)<br \/>\nh\u00b3 = 17<br \/>\nh = 17<\/p>\n<p>Question 27.<br \/>\n&#8211; 600 = \\(\\frac{2}{5}\\)k<sup>3<\/sup> + 750<\/p>\n<p>Answer:<br \/>\nk = -15<\/p>\n<p>Explanation:<br \/>\n(2\/5) = 0.4<br \/>\n-600 = 0.4 k\u00b3 + 750<br \/>\n0.4 k\u00b3 = -600 -750<br \/>\n0.4k\u00b3 = -1350<br \/>\nk\u00b3 = -(1350\/0.4)<br \/>\nk\u00b3 = -3375<br \/>\nk\u00b3 = -15\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nk = -15<\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe volume of a cube-shaped compost bin is 27 cubic feet. What is the edge length of the compost bin?<\/p>\n<p>Answer:<br \/>\nThe edge length of the compost bin = 3 feet.<\/p>\n<p>Explanation:<br \/>\nGiven that the volume of a cube-shaped compost bin = 27 cubic ft.<br \/>\nvolume of cube = s x sx s<br \/>\nvolume = 3 x 3 x3<br \/>\nvolume = 27<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe volume of a cube of ice for an ice sculpture is 64,000 cubic inches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-13.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 13\" width=\"287\" height=\"233\" \/><br \/>\na. What is the edge length of the cube of ice?<br \/>\nb. What is the surface area of the cube of ice?<\/p>\n<p>Answer:<br \/>\na. The edge length of the cube of ice = 40 inches.<br \/>\nb. The surface area of the cube of ice = 9600 sq in<\/p>\n<p>Explanation:<br \/>\na. The edge length of the cube of ice = 40 in<br \/>\nvolume = s x s x s<br \/>\nv = 40 x 40 x 40<br \/>\nv = 40 in<br \/>\nb. The surface area of cube\u00a0 = 6a\u00b2<br \/>\narea = 6 x 40 x 40<br \/>\nwhere a = edge<br \/>\narea = 6 x 1600<br \/>\narea = 9600 sq in<\/p>\n<p>Question 30.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nThere are three numbers that are their own cube roots. What are the numbers?<\/p>\n<p>Answer:<br \/>\n-1, 1 , 0<\/p>\n<p>Explanation:<br \/>\ncube root of -1 = -1<br \/>\ncube root of 1 = 1<br \/>\ncube root of 0 = 0<br \/>\nThe 3 numbers have their own cube roots.<\/p>\n<p><strong>REASONING<\/strong> Copy and complete the statement with &lt;, &gt;, or =.<br \/>\nQuestion 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-14.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 14\" width=\"117\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n-(1\/4) &lt;\u00a0 \u00a03\u221a(-8\/125)<\/p>\n<p>Explanation:<br \/>\n(1\/4) = -0.25<br \/>\n(8\/125) = (-2\/5)<br \/>\n(-2\/5) = 0.4<\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-15.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 15\" width=\"131\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n3\u221a 0.001 &gt;\u00a0 \u00a00.01<\/p>\n<p>Explanation:<br \/>\n3\u221a 0.001 = 0.1<br \/>\n0.1 &gt; 0.01<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-16.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 16\" width=\"135\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n3\u221a64 &lt; \u00a0 \u00a0\u221a64<\/p>\n<p>Explanation:<br \/>\n3\u221a64\u00a0 = 4 x 4 x4<br \/>\n3\u221a64\u00a0 = 4<br \/>\n\u221a64 = 8 x 8<br \/>\n\u221a64 = 8<br \/>\n4\u00a0 &lt;\u00a0 8<\/p>\n<p>Question 34.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou bake a dessert in the baking pan shown. You cut the dessert into cube-shaped pieces of equal size. Each piece has a volume of 8 cubic inches. How many pieces do you get from one pan? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-17.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 17\" width=\"180\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\n24 pieces.<\/p>\n<p>Explanation:<br \/>\nGiven that volume = 8 cubic inches<br \/>\ns = 2 in<br \/>\nArea = 64 sq in given<br \/>\narea = 6 x a\u00b2<br \/>\narea = 6 x 2 x2<br \/>\narea = 6 x 4<br \/>\narea = 24 sq in<\/p>\n<p>Question 35.<br \/>\n<strong>LOGIC<\/strong><br \/>\nDetermine whether each statement is true for square roots. Then determine whether each statement is true for cube roots. Explain your reasoning.<br \/>\na. You cannot find the square root of a negative number.<br \/>\nb. Every positive number has a positive square root and a negative square root.<\/p>\n<p>Answer:<br \/>\na.Yes<br \/>\nb. yes<\/p>\n<p>Explanation:<br \/>\na. we can find the square root of a negative number.<br \/>\nfor example -2<br \/>\nthe square root of -2 = -4<br \/>\nb. yes, every positive number\u00a0has a positive square root and a negative square root.<br \/>\nfor example = 4<br \/>\n-2 and 2 are the square roots of 4<\/p>\n<p>Question 36.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe pyramid has a volume of 972 cubic inches. What are the dimensions of the pyramid?<\/p>\n<p>Answer:<br \/>\nThe dimensions of the pyramid = 14 in<\/p>\n<p>Explanation:<br \/>\nGiven that volume of pyramid = 972 cubic in<br \/>\nvolume = ( l w h\/3)<br \/>\nvolume = (14 x 14 x 14\/3)<br \/>\nv = 972 cubic in<\/p>\n<p>Question 37.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe ratio 125 : x is equivalent to the ratio x<sup>2<\/sup> :125. What is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.3-18.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.3 18\" width=\"218\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nThe value of x = 25<\/p>\n<p>Explanation:<br \/>\nGiven that the ratio = 125 : x<br \/>\nx \u00b2 : 125\u00a0 = x = 25<br \/>\nwhen powers are equal exponents must be equal.<br \/>\nx = 25<\/p>\n<p><strong>CRITICAL THINKING<\/strong> Solve the equation.<br \/>\nQuestion 38.<br \/>\n(3x + 4)<sup>3<\/sup> = 2197<\/p>\n<p>Answer:<br \/>\nx = 6<\/p>\n<p>Explanation:<br \/>\n(3x + 4)<sup>3<\/sup> = 2197<br \/>\n9x\u00b3+ 64 = 2197<br \/>\n9x\u00b3 = 2197 &#8211; 64<br \/>\n9 x\u00b3 = 2133<br \/>\nx\u00b3 = (2133\/9)<br \/>\nx\u00b3 =\u00a0 237<br \/>\nx = 6<\/p>\n<p>Question 39.<br \/>\n(8x<sup>3<\/sup> &#8211; 9)<sup>3<\/sup> = 5832<\/p>\n<p>Answer:<br \/>\nx\u00b3 = 11.86<br \/>\nx = 3\/2<\/p>\n<p>Explanation:<br \/>\n512 x\u00b3 &#8211; 243 = 5832<br \/>\n512 x\u00b3 = 5832 + 243<br \/>\n512 x\u00b3 = 6075<br \/>\nx\u00b3 = 6075\/512<br \/>\nx\u00b3 = 11.86<\/p>\n<p>Question 40.<br \/>\n((5x &#8211; 16)<sup>3<\/sup> &#8211; 4)<sup>3<\/sup> = 216,000<\/p>\n<p>Answer:<br \/>\nx = 56<\/p>\n<p>Explanation:<br \/>\n125 x\u00b3 &#8211; 4096 &#8211; 64 = 216000<br \/>\n125 x\u00b3 &#8211; 4096 = 216000 + 64<br \/>\n125 x\u00b3 = 216064 + 4096<br \/>\n125 x\u00b3 = 220160<br \/>\nx\u00b3 = 1761.28<br \/>\nx = 56<\/p>\n<h3><a id=\"Lesson_9.4_Rational_Numbers\"><\/a>Lesson 9.4 Rational Numbers<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Work with a partner.<br \/>\na. Complete the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 1\" width=\"462\" height=\"391\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-1.png 462w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-1-300x254.png 300w\" sizes=\"(max-width: 462px) 100vw, 462px\" \/><br \/>\nb. For each row of the table, use the two equations and what you know about solving systems of equations to write a third equation that does not involve a repeating decimal. Then solve the equation. What does your solution represent?<br \/>\nc. Write each repeating decimal below as a fraction. How is your procedure similar to parts (a) and (b)? How is it different?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-2.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 2\" width=\"223\" height=\"111\" \/><br \/>\nd. Explain how to write a repeating decimal with n repeating digits as a fraction.<\/p>\n<p>Answer:<br \/>\na. x = 0.666 , 10 x = 10 x 0.666 = 6.666<br \/>\nx = 0.111, 10 x = 10 x0.111 = 1.111<br \/>\nx = 0.2444, 10 x = 10 x 0.24444 = 2.4444<br \/>\nc. x = (12\/100)<br \/>\nx = (0.45\/100)<br \/>\nx = (0.27\/100)<br \/>\nx = (0.940\/1000)<\/p>\n<p>Explanation:<br \/>\nGiven that x = 0.333<br \/>\n10 x = 10 x 0.333 = 3.3333<br \/>\nx = 0.666<br \/>\n10 x = 10 x 0.666 = 6.6666<br \/>\nx = 0.111<br \/>\n10 x = 10 x 0.111 = 1.111<br \/>\nx = 0.244<br \/>\n10 x = 10 x 0.244 = 2.444<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{3}{15}\\)<\/p>\n<p>Answer:<br \/>\n0.2<\/p>\n<p>Explanation:<br \/>\n(3\/15) = 0.2<\/p>\n<p>Question 2.<br \/>\n&#8211;\\(\\frac{2}{9}\\)<\/p>\n<p>Answer:<br \/>\n-0.222<\/p>\n<p>Explanation:<br \/>\n(-2\/9) = -0.222<\/p>\n<p>Question 3.<br \/>\n4\\(\\frac{3}{8}\\)<\/p>\n<p>Answer:<br \/>\n1.5<\/p>\n<p>Explanation:<br \/>\n(3\/8) = 0.375<br \/>\n4 x 0.375 = 1.5<\/p>\n<p>Question 4.<br \/>\n2\\(\\frac{6}{11}\\)<\/p>\n<p>Answer:<br \/>\n1.09<\/p>\n<p>Explanation:<br \/>\n(6\/11) = 0.5454<br \/>\n2 x 0.5454 = 1.0909<\/p>\n<p><strong>Write the decimal as a fraction or a mixed number.<\/strong><br \/>\nQuestion 5.<br \/>\n0.888 &#8230;..<\/p>\n<p>Answer:<br \/>\n(111\/125)<\/p>\n<p>Explanation:<br \/>\n0.888<br \/>\n(888\/1000)<br \/>\n(444\/500)<br \/>\n(222\/250)<br \/>\n(111\/125)<\/p>\n<p>Question 6.<br \/>\n\\(2.0 \\overline{6}\\)<\/p>\n<p>Answer:<br \/>\n(33\/100)<\/p>\n<p>Explanation:<br \/>\n(2.0 \/6)<br \/>\n0.333<br \/>\n(33\/100)<\/p>\n<p>Question 7.<br \/>\n\\(0 . \\overline{64}\\)<\/p>\n<p>Answer:<br \/>\n0<\/p>\n<p>Explanation:<br \/>\n(0\/64)<br \/>\n64<\/p>\n<p>Question 8.<br \/>\n\\(-4 . \\overline{50}\\)<\/p>\n<p>Answer:<br \/>\n-(8\/100)<\/p>\n<p>Explanation:<br \/>\n-4 \/50<br \/>\n&#8211; 0.08<br \/>\n-8\/100<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow can you identify a rational number?<\/p>\n<p>Answer:<br \/>\nA rational number is a number that can be written as a ratio, which means it can be written as a fraction, in which both the numerator and denominator are whole numbers.<\/p>\n<p>Explanation:<br \/>\n8<br \/>\n(8\/1)<br \/>\nthe number 8 is a rational number because the number written as a fraction.<\/p>\n<p><strong>WRITING FRACTIONS OR MIXED NUMBERS AS DECIMALS<\/strong> Write the fraction or mixed number as a decimal.<br \/>\nQuestion 10.<br \/>\n\\(\\frac{9}{50}\\)<\/p>\n<p>Answer:<br \/>\n0.18<\/p>\n<p>Explanation:<br \/>\n(9\/50)<br \/>\n(9\/50) = 0.18<\/p>\n<p>Question 11.<br \/>\n&#8211; \\(\\frac{7}{18}\\)<\/p>\n<p>Answer:<br \/>\n-0.388<\/p>\n<p>Explanation:<br \/>\n-(7\/18)<br \/>\n-(7\/18) = -0.388<\/p>\n<p>Question 12.<br \/>\n3\\(\\frac{4}{9}\\)<\/p>\n<p>Answer:<br \/>\n1.333<\/p>\n<p>Explanation:<br \/>\n(4\/9)<br \/>\n4\/9 = 0.444<br \/>\n3 x 0.444<br \/>\n1.333<\/p>\n<p>Question 13.<br \/>\n&#8211; 12 \\(\\frac{1}{6}\\)<\/p>\n<p>Answer:<br \/>\n&#8211; 1.9992<\/p>\n<p>Explanation:<br \/>\n(1\/6)<br \/>\n(1\/6) = 0.1666<br \/>\n0.1666 x -12<br \/>\n-1.9992<\/p>\n<p><strong>WRITING A REPEATING DECIMAL AS A FRACTION<\/strong> Write the repeating decimal as a fraction or a mixed number.<br \/>\nQuestion 14.<br \/>\n\\(-1 . \\overline{7}\\)<\/p>\n<p>Answer:<br \/>\n(-1\/7)<\/p>\n<p>Explanation:<br \/>\n-1: 7<br \/>\n-(1\/7)<\/p>\n<p>Question 15.<br \/>\n\\(0 . \\overline{2}\\)<\/p>\n<p>Answer:<br \/>\n(0\/2)<\/p>\n<p>Explanation:<br \/>\n0 : 2<br \/>\n(0\/2)<\/p>\n<p>Question 16.<br \/>\n\\(8 . \\overline{93}\\)<\/p>\n<p>Answer:<br \/>\n(8 \/93)<\/p>\n<p>Explanation:<br \/>\n8 : 93<br \/>\n(8\/93)<\/p>\n<p>Question 17.<br \/>\n\\(-6 . \\overline{235}\\)<\/p>\n<p>Answer:<br \/>\n-(6\/235)<\/p>\n<p>Explanation:<br \/>\n-6 : 235<br \/>\n-(6 \/235)<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 18.<br \/>\nA fun house mirror distorts the image it reflects. Objects reflected in the mirror appear \\(1 . \\overline{3}\\) times taller. When a five-foot-tall person looks in the mirror, how tall does he appear?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-3.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 3\" width=\"175\" height=\"161\" \/><\/p>\n<p>Answer:<br \/>\nHe appears in the mirror\u00a0 = 5 feet.<\/p>\n<p>Explanation:<br \/>\n1 x 3 = 3 given that<br \/>\n1 x 5 = 5<\/p>\n<p>Question 19.<br \/>\nAn exchange rate represents the value of one currency relative to another. Your friend visits a country that uses a local currency with an exchange rate of \\(1 . \\overline{265}\\) units of the local currency to $1. If a bank charges $2 to change currency, how many units of the local currency does your friend receive when she gives the bank $200?<\/p>\n<p>Answer:<br \/>\nFriend receive local currency = 1,06,000 units.<\/p>\n<p>Explanation:<br \/>\nGiven that local currency of $1 = 265 units.<br \/>\nif a bank charges to $ 2<br \/>\n265 + 265 = 530<br \/>\nthe local currency of the friend receive when she gives the bank $ 200<br \/>\n200 x 530<br \/>\n1,06,000 units.<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA low fuel warning appears when a particular car has \\(0.014 \\overline{6}\\) 6 of a tank of gas remaining. The car holds 18.5 gallons of gas and can travel 36 miles for each gallon used. How many miles can the car travel after the low fuel warning appears?<\/p>\n<p>Answer:<br \/>\n9.324 gallons.<\/p>\n<p>Explanation:<br \/>\n(0.014\/6) = 0.0023<br \/>\n0.0023 x 6<br \/>\n0.014<br \/>\nGiven that car holds 18.5 gallons of gas can travel 36 miles for each gallon.<br \/>\n36 x 0.014<br \/>\n0.504<br \/>\n0.504 x 18.5 gallons<br \/>\n9.324 gallons.<\/p>\n<h3><a id=\"Rational_Numbers_Homework_&amp;_Practice_9.4\"><\/a>Rational Numbers Homework &amp; Practice 9.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n2 + \\(\\sqrt [ 3 ]{ 27 } \\)<\/p>\n<p>Answer:<br \/>\n5<\/p>\n<p>Explanation:<br \/>\ncube root of (27) is (3)<br \/>\n3\u221a27 = (3) x (3) x (3)<br \/>\n27\u00b3 = (3)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n27 = 3<br \/>\n2 + 3<br \/>\n5<\/p>\n<p>Question 2.<br \/>\n1 &#8211; \\(\\sqrt [ 3 ]{ 8 } \\)<\/p>\n<p>Answer:<br \/>\n-1<\/p>\n<p>Explanation:<br \/>\ncube root of (8) is (2)<br \/>\n3\u221a8 = (2) x (2) x (2)<br \/>\n8\u00b3 = (2)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n8 = 2<br \/>\n1- 2<br \/>\n-1<\/p>\n<p>Question 3.<br \/>\n7\\(\\sqrt [ 3 ]{ 125 } \\) &#8211; 12<\/p>\n<p>Answer:<br \/>\n23<\/p>\n<p>Explanation:<br \/>\ncube root of (125) is (5)<br \/>\n3\u221a125 = (5) x (5) x (5)<br \/>\n125\u00b3 = (5)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n125 = 5<br \/>\n7 x 5 -12<br \/>\n35 -12<br \/>\n23<\/p>\n<p><strong>Find the measures of the interior angles of the triangle.<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-4.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 4\" width=\"160\" height=\"61\" \/><\/p>\n<p>Answer:<br \/>\nx = 75\u2070<\/p>\n<p>Explanation:<br \/>\nRight angle triangle = 90\u2070<br \/>\nx = 90\u2070 &#8211; 15\u2070<br \/>\ngiven that 75\u2070<br \/>\nx = 75\u2070<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-5.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 5\" width=\"145\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nx = 80\u2070<\/p>\n<p>Explanation:<br \/>\nx + 40\u2070 = 60\u2070<br \/>\nx = 60\u2070 +40\u2070 +80<br \/>\nx = 80\u2070<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-6.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 6\" width=\"173\" height=\"81\" \/><br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\ngiven that (x &#8211; 5)\u2070 = 140\u2070<br \/>\nx &#8211; 5\u2070 = 140\u2070<br \/>\nx = 140\u2070 + 5\u2070<br \/>\nx = 145\u2070<br \/>\n2x = 145\u2070 x 2<br \/>\n2x = 290\u2070<br \/>\nx = 290\u2070\/2<br \/>\nx = 145\u2070<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>WRITING REPEATING DECIMALS AS FRACTIONS<\/strong> Write the repeating decimal as a fraction. (See Exploration 1, p. 395.)<br \/>\nQuestion 7.<br \/>\n0.777 . . .<\/p>\n<p>Answer:<br \/>\n(7\/9)<\/p>\n<p>Explanation:<br \/>\n0.7777. . .<br \/>\n(7\/9)<\/p>\n<p>Question 8.<br \/>\n0.858585 . . .<\/p>\n<p>Answer:<br \/>\n(85\/99)<\/p>\n<p>Explanation:<br \/>\n0.858585 . . .<br \/>\n(85\/99)<\/p>\n<p>Question 9.<br \/>\n0.232323 . . .<\/p>\n<p>Answer:<br \/>\n(23\/99)<\/p>\n<p>Explanation:<br \/>\n0.232323 . . .<br \/>\n(23\/99)<br \/>\nit is a repeating decimal<\/p>\n<p><strong>WRITING FRACTIONS OR MIXED NUMBERS AS DECIMALS<\/strong> Write the fraction or mixed number as a decimal.<br \/>\nQuestion 10.<br \/>\n&#8211;\\(\\frac{3}{20}\\)<\/p>\n<p>Answer:<br \/>\n-0.15<\/p>\n<p>Explanation:<br \/>\n(3\/20) = 0.15<\/p>\n<p>Question 11.<br \/>\n9\\(\\frac{1}{12}\\)<\/p>\n<p>Answer:<br \/>\n9.083<\/p>\n<p>Explanation:<br \/>\n(1\/12) = 0.833<br \/>\n0.833 x 9 = 9.083<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{5}{36}\\)<\/p>\n<p>Answer:<br \/>\n0.1388<\/p>\n<p>Explanation:<br \/>\n(5\/36) = 0.1388<\/p>\n<p>Question 13.<br \/>\n6\\(\\frac{1}{40}\\)<\/p>\n<p>Answer:<br \/>\n6.025<\/p>\n<p>Explanation:<br \/>\n(1\/40) = 0.025<br \/>\n6 x 0.025<br \/>\n6.025<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{11}{75}\\)<\/p>\n<p>Answer:<br \/>\n0.1466<\/p>\n<p>Explanation:<br \/>\n(11\/75)<br \/>\n0.1466<\/p>\n<p>Question 15.<br \/>\n&#8211; 2\\(\\frac{7}{18}\\)<\/p>\n<p>Answer:<br \/>\n-2.38<br \/>\nExplanation:<br \/>\n(17\/18)<br \/>\n0.3888<br \/>\n-2 x 0.3888<br \/>\n-2.38<\/p>\n<p>Question 16.<br \/>\n<strong>PRECISION<\/strong><br \/>\nYour hair is \\(\\frac{5}{16}\\) inch long. Write this length as a decimal.<\/p>\n<p>Answer:<br \/>\n0.3125 in<\/p>\n<p>Explanation:<br \/>\n(5\/16)<br \/>\n0.3125<\/p>\n<p><strong>WRITING A REPEATING DECIMAL AS A FRACTION<\/strong> Write the repeating decimal as a fraction or a mixed number.<br \/>\nQuestion 17.<br \/>\n\\(-0 . \\overline{5}\\)<\/p>\n<p>Answer:<br \/>\n-5\/9<\/p>\n<p>Explanation:<br \/>\n-5\/9<\/p>\n<p>Question 18.<br \/>\n\\(4 . \\overline{1}\\)<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\n4 x 1<br \/>\n4<\/p>\n<p>Question 19.<br \/>\n\\(-0.3 \\overline{56}\\)<\/p>\n<p>Answer:<br \/>\n-353\/990<br \/>\nExplanation:<br \/>\n-0.3 x 56<br \/>\n-26.7<br \/>\n-(353\/990)<\/p>\n<p>Question 20.<br \/>\n\\(6.0 \\overline{89}\\)<\/p>\n<p>Answer:<br \/>\n(674\/1000)<\/p>\n<p>Explanation:<br \/>\n(6\/89)<br \/>\n0.0674<br \/>\n(674\/1000)<\/p>\n<p>Question 21.<br \/>\n\\(0.18 \\overline{72}\\)<\/p>\n<p>Answer:<br \/>\n103\/550<br \/>\nExplanation:<br \/>\n(0.18\/72)<br \/>\n103\/550<\/p>\n<p>Question 22.<br \/>\n\\(11 . \\overline{510}\\)<\/p>\n<p>Answer:<br \/>\n(2156\/10000)<\/p>\n<p>Explanation:<br \/>\n(11\/510)<br \/>\n0.02156<br \/>\n(2156\/10000)<\/p>\n<p>Question 23.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nA forecast cone defines the probable path of a tropical cyclone. The probability that the center of a particular tropical cyclone remains within the forecast cone is \\(0 . \\overline{8}\\). Write this probability as a fraction.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-7.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 7\" width=\"160\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\n8 : 9<\/p>\n<p>Explanation:<br \/>\nGiven that cone is 8 x 9<br \/>\nthey said to write it in the fraction.<\/p>\n<p>Question 24.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nDescribe how to write a decimal with 12 repeating digitsas a fraction.<\/p>\n<p>Answer:<br \/>\n12: 0<\/p>\n<p>Explanation:<br \/>\ngiven that 12 is a decimal<br \/>\nand they said to write in decimal.<br \/>\n12 : 0<\/p>\n<p>Question 25.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nAn approximation for the value of \u03c0 is \\(\\frac{22}{7}\\). Write this number as a repeating decimal.<\/p>\n<p>Answer:<br \/>\n3.14 2857<\/p>\n<p>Explanation:<br \/>\n\u03c0 = (22\/7)<br \/>\n(22\/7) = 3.14<br \/>\n3.142857<\/p>\n<p>Question 26.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe density of iodine is about \\(6.28 \\overline{1}\\) times the density of acetone. The density of acetone is about 785 kilograms per cubic meter. What is the density of iodine? Write your answer as a repeating decimal.<\/p>\n<p>Answer:<br \/>\n4929.8. . .<\/p>\n<p>Explanation:<br \/>\nThe density of iodine = 6.28 given<br \/>\nthe density of acetone is 785 kg for cubic meter.<br \/>\n6.28 x 785<br \/>\n4,929.8<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA disinfectant manufacturer suggests that its product kills \\(99.9 \\overline{8}\\) % of germs. Write this percent as a repeating decimal and then as a fraction. How many germs would survive when the disinfectant is applied to an object with 18,000 germs?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-8.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 8\" width=\"126\" height=\"281\" \/><\/p>\n<p>Answer:<br \/>\nFraction = (8999\/9000)<br \/>\n2 germs<\/p>\n<p>Explanation:<br \/>\nGiven that the product kills (99.9\/8)%<br \/>\n8999\/9000<br \/>\n2 germs<br \/>\nQuestion 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou and your friend are making pear tarts for a bake sale. Your recipe uses \\(\\frac{7}{6}\\) times the weight of the diced pears used in your friend\u2019s recipe. Your friend\u2019s recipe calls for 0.3 pound of diced pears. How many pounds of pears should you buy to have enough for both recipes?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-9.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 9\" width=\"132\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\n0.35 pounds of pears should buy to have enough for both recipes.<\/p>\n<p>Explanation:<br \/>\nGiven that my recipe uses (7\/6) times the weight of the diced pears used in friends recipe.<br \/>\nmy friends recipie calls for 0.3 pounds of diced pears.<br \/>\n(7\/6) x 0.3<br \/>\n1.16666 x 0.3<br \/>\n0.35 pounds<\/p>\n<p>Question 29.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe table shows the principal and interest earned per year for each of three savings accounts with simple annual interest. Which account has the greatest interest rate? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-10.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 10\" width=\"641\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-10.png 641w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-10-300x57.png 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><\/p>\n<p>Answer:<br \/>\nAccount c has the greatest interest rate.<\/p>\n<p>Explanation:<br \/>\nSimple interest = (px r x t \/100)<br \/>\nwhere p = principal amount, rate of interest, and time = t<br \/>\nAccount A = $ 4\/$90 =0.04 = 4.4 %<br \/>\nAccount B = $5.50\/$120.00 = 0.04583 = 4.583%<br \/>\nAccount C = $4.80\/$100.00 = 0.048 = 4.8%<\/p>\n<p>Question 30.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe probability that an athlete makes a half-court basketball shot is 22 times the probability that the athlete makes a three-quarter-court shot. The probability that the athlete makes three-quarter-court shot is \\(0.00 \\overline{9}\\). What is the probability that the athlete makes a half-court shot? Write your answer as a percent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.4-11.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.4 11\" width=\"119\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\n1.98 %<\/p>\n<p>Explanation:<br \/>\nGiven that the athlete makes three-quarter-court shot is 0.00 x 9<br \/>\nbasketball shot is 22 times the probability that the athlete makes 3 -quarter-court shot.<br \/>\n0.00 x 9<br \/>\n0<br \/>\n22 x 9<br \/>\n198 writing it as decimal<br \/>\n1.98%<br \/>\n<strong>NUMBER SENSE<\/strong> Determine whether the numbers are equal. Justify your answer.<br \/>\nQuestion 31.<br \/>\n\\(\\frac{9}{22}\\) and \\(0.4 \\overline{09}\\)<\/p>\n<p>Answer:<br \/>\nThe numbers are not equal.<\/p>\n<p>Explanation:<br \/>\n(9\/22) = 0.4090<br \/>\n(0.4\/9)\u00a0 = 0.0444<\/p>\n<p>Question 32.<br \/>\n\\(\\frac{1}{999}\\) and 0<\/p>\n<p>Answer:<br \/>\nThe numbers are not equal.<\/p>\n<p>Explanation:<br \/>\n(1\/999) = 0.001<br \/>\n0 = 0.001<\/p>\n<p>Question 33.<br \/>\n\\(\\frac{135}{90}\\) and 1.5<\/p>\n<p>Answer:<br \/>\nThe numbers are not equal.<\/p>\n<p>Explanation:<br \/>\n(35\/90) = 1.5<br \/>\n1.5 = 1.5<\/p>\n<p><strong>ADDING AND SUBTRACTING RATIONAL NUMBERS<\/strong> Add or subtract.<br \/>\nQuestion 34.<br \/>\n\\(0.4 \\overline{09}+0.6 \\overline{81}\\)<\/p>\n<p>Answer:<br \/>\n0.45180<\/p>\n<p>Explanation:<br \/>\n(0.4\/9) = .04444<br \/>\n(0.6\/81) = 0.0074<br \/>\n0.0074 +0.444<\/p>\n<p>Question 35.<br \/>\n\\(-0 . \\overline{63}+\\frac{5}{99}\\)<\/p>\n<p>Answer:<br \/>\n-58\/99<\/p>\n<p>Explanation:<br \/>\n(5\/99) = 0.0505<br \/>\n63 + 0.0505<\/p>\n<p>Question 36.<br \/>\n\\(\\frac{11}{6}-0 . \\overline{27}\\)<\/p>\n<p>Answer:<br \/>\n-25.1666<\/p>\n<p>Explanation:<br \/>\n(11\/6) = 1.833333<br \/>\n27<br \/>\n1.83333\u00a0 &#8211; 27<br \/>\n-25.1666<\/p>\n<p>Question 37.<br \/>\n\\(0 . \\overline{03}-0 . \\overline{04}\\)<\/p>\n<p>Answer:<br \/>\n-1\/99<\/p>\n<p>Question 38.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nWrite a repeating decimal that is between \\(\\frac{9}{7}\\) and \\(\\frac{10}{7}\\). Justify your answer.<\/p>\n<p>Answer:<br \/>\n1.3546<\/p>\n<p>Explanation:<br \/>\n(9\/7)<br \/>\n1.2857<br \/>\n(10\/7)<br \/>\n1.4285<br \/>\nThe number between 1.2857 and 1.4285 is 1.3546<\/p>\n<h3><a id=\"Lesson_9.5_Irrational_Numbers\"><\/a>Lesson 9.5 Irrational Numbers<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Approximating Square Roots<br \/>\nWork with a partner. Use the square shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 1\" width=\"460\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-1.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-1-300x114.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><br \/>\na. Find the exact length x of the diagonal. Is this number a number a rational number or an irrational number? Explain.<br \/>\nb. The value of x is between which two whole numbers? Explain your reasoning.<br \/>\nc. Use the diagram below to approximate the length of the diagonal to the nearest tenth.Explain your method.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 2\" width=\"556\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-2.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-2-300x87.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\nd. Which of the following is the closest approximation of the length of the diagonal? Justify your answer using inverse operations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 3\" width=\"387\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-3.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-3-300x43.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\nAnswer:<br \/>\na. The length of x = \u221a2<br \/>\na number is an irrational number.<br \/>\nd. 1.412 is the closest approximation of the length of the diagonal.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Classify the real number.<\/strong><br \/>\nQuestion 1.<br \/>\n0.121221222 &#8230;&#8230;<\/p>\n<p>Answer:<br \/>\nIrrational number.<\/p>\n<p>Explanation:<br \/>\nIrrational number : the decimal form neither terminates nor repeats.<br \/>\nso the given number is a irrational number.<\/p>\n<p>Question 2.<br \/>\n&#8211; \u221a196<br \/>\nAnswer:<br \/>\nThe number is real number<\/p>\n<p>Explanation:<br \/>\nthe real number are the numbers which includes both rational and irrational numbers.<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt [ 3 ]{ 2 } \\)<\/p>\n<p>Answer:<br \/>\nThe number is real number<\/p>\n<p>Explanation:<br \/>\ncube root of 3 is 2<br \/>\nwhere cube and cube root get cancelled.<\/p>\n<p><strong>Approximate the number to the nearest (a) integer and (b) tenth.<\/strong><br \/>\nQuestion 4.<br \/>\n\u221a8<\/p>\n<p>Answer:<br \/>\nInteger = 3<br \/>\ntenth = 3 .0<\/p>\n<p>Explanation:<br \/>\nsquare root of 8 = 2 x 2 x2<br \/>\n2 x2 = 4<br \/>\n3 is nearest integer to the 2<\/p>\n<p>Question 5.<br \/>\n&#8211; \u221a13<\/p>\n<p>Answer:<br \/>\n-14<\/p>\n<p>Question 6.<br \/>\n&#8211; \u221a24<br \/>\nAnswer:<br \/>\n13<\/p>\n<p>Question 7.<br \/>\n\u221a20<br \/>\nAnswer:<br \/>\n11<\/p>\n<p><strong>Which number is greater? Explain.<\/strong><br \/>\nQuestion 8.<br \/>\n\u221a8, \u03c0<\/p>\n<p>Answer:<br \/>\n\u221a8 is greater.<\/p>\n<p>Explanation:<br \/>\n\u221a8 = 8<br \/>\n\u03c0 = 3.14<br \/>\nso 8 is greater.<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 3 ]{ 65 }\\), \u221a26<\/p>\n<p>Answer:<br \/>\n\u221a26 is greater.<\/p>\n<p>Explanation:<br \/>\ncube root of 65 = 4 x 4 x4<br \/>\nsquare root of 26 = 26<br \/>\n26 is greater.<\/p>\n<p>Question 10.<br \/>\n&#8211; \u221a2, &#8211; \\(\\sqrt [ 3 ]{ 10 }\\)<br \/>\nAnswer:<br \/>\n10 is greater.<\/p>\n<p>Explanation:<br \/>\ncube root of 10 = 10<br \/>\nsquare root of -2 = -2<br \/>\nsoo 10 is greater.<\/p>\n<p><strong>Approximate the distance between the points to the nearest tenth.<\/strong><br \/>\nQuestion 11.<br \/>\n(- 3, &#8211; 1) and (- 2, &#8211; 2)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n(1, &#8211; 1) and (5, 4)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n(5, 4) and (9, 8)<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n(- 7, 10) and (3, &#8211; 5)<br \/>\nAnswer:<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 15.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow are rational numbers and irrational numbers different?<\/p>\n<p>Answer:<br \/>\nrational number: a rational number is a number such as -3\/7 that can be expressed as the quotient or fractionp\/q of two integers, a numerator p, and non zero denominator q. Every integer is a rational number.<br \/>\nirrational number: irrational numbers are all the real numbers that are not rational numbers.<\/p>\n<p>Explanation:<br \/>\nrational number: a rational number is a number such as -3\/7 that can be expressed as the quotient or fractionp\/q of two integers, a numerator p, and non zero denominator q. Every integer is a rational number.<br \/>\nirrational number: irrational numbers are all the real numbers that are not rational numbers.<\/p>\n<p><strong>CLASSIFYING REAL NUMBERS<\/strong> Classify the real number.<br \/>\nQuestion 16.<br \/>\n\\(\\frac{48}{16}\\)<br \/>\nAnswer:<br \/>\nReal number<\/p>\n<p>Explanation:<br \/>\n(48\/16) = 3<br \/>\n3 is a real number.<\/p>\n<p>Question 17.<br \/>\n&#8211; \u221a76<br \/>\nAnswer:<br \/>\nIrrational numbers<\/p>\n<p>Explanation:<br \/>\n76 is irrational number<br \/>\nirrational numbers are real numbers.<\/p>\n<p>Question 18.<br \/>\n\\(\\sqrt [ 3 ]{ -216 }\\)<\/p>\n<p>Answer:<br \/>\n-6 is a rational number.<\/p>\n<p>Explanation:<br \/>\ncube root of 216 = -6<\/p>\n<p><strong>APPROXIMATING AN IRRATIONAL NUMBER<\/strong> Approximate the number to the nearest (a) integer and (b) tenth.<br \/>\nQuestion 19.<br \/>\n\u221a51<br \/>\nAnswer:<br \/>\n26<\/p>\n<p>Question 20.<br \/>\n&#8211; \u221a87<br \/>\nAnswer:<br \/>\n44<\/p>\n<p>Question 21.<br \/>\n\\(\\sqrt [ 3 ]{ 60 }\\)<br \/>\nAnswer:<br \/>\n5<\/p>\n<p>Question 22.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich number does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 4\" width=\"350\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-4.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-4-300x49.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<p>Answer:<br \/>\n-3.3 is different from the three.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 23.<br \/>\nThe equation 3600b<sup>2<\/sup> = hw represents the relationship among the body surface area b (in square meters), height h (in centimeters), and weight w (in kilograms) of a person. To the nearest tenth, approximate the body surface area of a person who is 168 centimeters tall and weighs 60 kilograms.<\/p>\n<p>Answer:<br \/>\n2.8 cm<\/p>\n<p>Explanation:<br \/>\nGiven that the surface area of a person = 168 cm<br \/>\nw = 60<br \/>\n3600 b\u00b2 = 168 x 60<br \/>\n3600 b\u00b2 = 10080<br \/>\nb\u00b2 = (10080\/3600)<br \/>\nb\u00b2 = 2.8<\/p>\n<p>Question 24.<br \/>\nWhich plane is closer to the base of the airport tower? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 5\" width=\"609\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-5.png 609w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-5-300x81.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><\/p>\n<p>Answer:<br \/>\nPlane B is closer to the base of the airport tower.<\/p>\n<h3><a id=\"Irrational_Numbers_Homework_&amp;_Practice_9.5\"><\/a>Irrational Numbers Homework &amp; Practice 9.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write the repeating decimal as a fraction or a mixed number.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(0 . \\overline{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(1.0 \\overline{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\\(0 . \\overline{75}\\)<\/p>\n<p>Answer:<\/p>\n<p>Question 4.<br \/>\n\\(2 . \\overline{36}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression. Write your answer as a power.<\/strong><br \/>\nQuestion 5.<br \/>\n(5<sup>4<\/sup>)<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n5 \u2078<\/p>\n<p>Explanation:<br \/>\n(5<sup>4<\/sup>)<sup>2<br \/>\n5 \u2078 = 5 x 5 x 5 x 5 x5 x5 x5<br \/>\n<\/sup>5\u2078<\/p>\n<p>Question 6.<br \/>\n(- 9)<sup>4<\/sup> . (- 9)<sup>7<\/sup><\/p>\n<p>Answer:<br \/>\n(-9)\u00b9\u00b9<\/p>\n<p>Explanation:<br \/>\n(-9)\u2074 . (-9)\u2077<br \/>\nwhen exponents are equal powers must be added.<br \/>\n(-9)\u2074 +\u2077<br \/>\n(-9)\u00b9\u00b9<\/p>\n<p>Question 7.<br \/>\na<sup>8<\/sup> . a<\/p>\n<p>Answer:<br \/>\na\u2079<\/p>\n<p>Explanation:<br \/>\n(a)\u2078 . (a)\u00b9<br \/>\nwhen exponents are equal powers must be added.<br \/>\n(a)\u2078 +\u00b9<br \/>\n(a)\u2079<\/p>\n<p>Question 8.<br \/>\n(y<sup>3<\/sup>)<sup>6<\/sup><\/p>\n<p>Answer:<br \/>\ny \u2076<\/p>\n<p>Explanation:<br \/>\ncube root of y = y x y x y<br \/>\ny \u2076<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>APPROXIMATING SQUARE ROOTS<\/strong> Find the exact length x of the diagonal of the square or rectangle. The value of x is between which two whole numbers? (See Exploration 1, p. 401.)<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 6\" width=\"126\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nx = 18<\/p>\n<p>Explanation:<br \/>\nGiven that the sides of a square = s x s<br \/>\nsquare =2 3 x 3<br \/>\ns = 18<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 7\" width=\"158\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\nx = 24<\/p>\n<p>Explanation:<br \/>\nGiven that the sides of a rectangle\u00a0 = 2 (l + b)<br \/>\nrectangle = 2( 8 + 4)<br \/>\nrectangle = 2(12)<br \/>\nrectangle = 24<\/p>\n<p><strong>CLASSIFYING REAL NUMBERS<\/strong> Classify the real number.<br \/>\nQuestion 11.<br \/>\n0<br \/>\nAnswer:<br \/>\nwhole<br \/>\ninteger<br \/>\nrational<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt [ 3 ]{ 343 }\\)<\/p>\n<p>Answer:<br \/>\n7<\/p>\n<p>Explanation:<br \/>\ncube root of 343 = 7 x 7 x 7<br \/>\n7<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{\u03c0}{6}\\)<\/p>\n<p>Answer:<br \/>\n18.84<br \/>\nirrational number.<\/p>\n<p>Question 14.<br \/>\n&#8211; \u221a81<\/p>\n<p>Answer:<br \/>\n-9<\/p>\n<p>Explanation:<br \/>\nsquare root of -81 = -9 x -9<\/p>\n<p>Question 15.<br \/>\n&#8211; 1.125<\/p>\n<p>Answer:<br \/>\nrational number<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{52}{13}\\)<\/p>\n<p>Answer:<br \/>\n676<\/p>\n<p>Explanation:<br \/>\n(52\/13)<br \/>\n676<\/p>\n<p>Question 17.<br \/>\n\\(\\sqrt [ 3 ]{ -49 }\\)<\/p>\n<p>Answer:<br \/>\n-7<br \/>\nirrational<\/p>\n<p>Question 18.<br \/>\n\u221a15<\/p>\n<p>Answer:<br \/>\n15<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend classifies \u221a144. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 8\" width=\"166\" height=\"68\" \/><\/p>\n<p>Answer:<br \/>\nNo<\/p>\n<p>Explanation:<br \/>\n144 is a perfect square.<br \/>\nsquare root of 144 is rational number.<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou cut a photograph into a right triangle for a scrapbook. The lengths of the legs of the triangle are 4 inches and 6 inches. Is the length of the hypotenuse a rational number? Explain.<\/p>\n<p>Answer:<br \/>\n\u221a52<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n4\u00b2 + 6\u00b2 = c\u00b2<br \/>\n16 + 36 = c\u00b2<br \/>\n52 = c\u00b2<br \/>\nc =\u221a52<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nPlace each number in the correct area of the Venn diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 9\" width=\"325\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-9.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-9-300x150.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\na. the last digit of your phone number<br \/>\nb. the square root of any prime number<br \/>\nc. the quotient of the circumference of a circle and its diameter<\/p>\n<p>Answer:<br \/>\nb. irrational number.<br \/>\nc. irrational number.<\/p>\n<p><strong>APPROXIMATING AN IRRATIONAL NUMBER<\/strong> Approximate the number to the nearest (a) integer and (b) tenth.<br \/>\nQuestion 22.<br \/>\n\u221a46<\/p>\n<p>Answer:<br \/>\na. 46<br \/>\nb.\u221a36<\/p>\n<p>Explanation:<br \/>\nsquare root of 46 = 46<br \/>\nnearest tenth = 36<br \/>\n46 &#8211; 10 = 36<\/p>\n<p>Question 23.<br \/>\n&#8211; \u221a105<\/p>\n<p>Answer:<br \/>\na.-10<br \/>\nb.-10 .2<\/p>\n<p>Explanation:<br \/>\nsquare root of -105 = -10<br \/>\nnearest tenth = -10.2<br \/>\nQuestion 24.<br \/>\n\\(\\sqrt [ 3 ]{ -12 }\\)<\/p>\n<p>Answer:<br \/>\na.\u00b3\u221a-12<br \/>\nb..\u00b3\u221a-2<\/p>\n<p>Explanation:<br \/>\nsquare root of -12= -12<br \/>\nnearest tenth = -2<br \/>\n12 &#8211; 10 = 2<\/p>\n<p>Question 25.<br \/>\n\\(\\sqrt [ 3 ]{ 310 }\\)<\/p>\n<p>Answer:<br \/>\na. 7<br \/>\nb. 6.8<\/p>\n<p>Explanation:<br \/>\ncube root of 310 = 7<br \/>\nnearest tenth = 7<br \/>\n6.8<\/p>\n<p>Question 26.<br \/>\n\\(\\sqrt{\\frac{27}{4}}\\)<\/p>\n<p>Answer:<br \/>\n6.75<br \/>\n6.65<\/p>\n<p>Explanation:<br \/>\n(27\/4)<br \/>\n6.75<br \/>\n6.75 &#8211; 10 = 6.65<\/p>\n<p>Question 27.<br \/>\n\\(-\\sqrt{\\frac{335}{2}}\\)<\/p>\n<p>Answer:<br \/>\n-13<br \/>\n12.9<\/p>\n<p>Explanation:<br \/>\n(335\/2)<br \/>\n-13<br \/>\n-13 &#8211; 10<br \/>\n-12.9<\/p>\n<p><strong>COMPARING IRRATIONAL NUMBERS<\/strong> Which number is greater? Explain.<br \/>\nQuestion 28.<br \/>\n\u221a125, \u221a135<\/p>\n<p>Answer:<br \/>\n\u221a135<\/p>\n<p>Explanation:<br \/>\n135 is greater than 125<\/p>\n<p>Question 29.<br \/>\n\u221a22, \\(\\sqrt [ 3 ]{ 34 }\\)<\/p>\n<p>Answer:<br \/>\n34<\/p>\n<p>Explanation:<br \/>\n34 is greater then 22<\/p>\n<p>Question 30.<br \/>\n&#8211; \\(\\sqrt [ 3 ]{ 100 }\\), &#8211; \u221a42<\/p>\n<p>Answer:<br \/>\n-42<\/p>\n<p>Explanation:<br \/>\n-42 is greater than -100<\/p>\n<p>Question 31.<br \/>\n\u221a5, \u03c0<\/p>\n<p>Answer:<br \/>\n\u221a5<\/p>\n<p>Explanation:<br \/>\n5 is greater than 3.14<\/p>\n<p>Question 32.<br \/>\n\\(\\sqrt [ 3 ]{ 130 }\\), \u221a28<\/p>\n<p>Answer:<br \/>\n130<\/p>\n<p>Explanation:<br \/>\n130 is greater than 28<\/p>\n<p>Question 33.<br \/>\n&#8211; \u221a38, \\(\\sqrt [ 3 ]{ -250 }\\)<\/p>\n<p>Answer:<br \/>\n-250<\/p>\n<p>Explanation:<br \/>\n250 is greater than 38<\/p>\n<p><strong>USING TOOLS<\/strong> Use the graphing calculator screen to determine whether the statement is true or false.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 10\" width=\"185\" height=\"121\" \/><br \/>\nQuestion 34.<br \/>\nTo the nearest tenth, \u221a10 = 3.1.<\/p>\n<p>Answer:<br \/>\n3.16227766<\/p>\n<p>Question 35.<br \/>\nThe value of \u221a14 is between 3.74 and 3.75.<\/p>\n<p>Answer:<br \/>\nTrue<\/p>\n<p>Explanation:<br \/>\nGiven that the \u221a14 = 3.74165<\/p>\n<p>Question 36.<br \/>\n\u221a10 lies between 3.1 and 3.16 on a number line.<\/p>\n<p>Answer:<br \/>\nTrue<\/p>\n<p>Explanation:<br \/>\nGiven that the \u221a10 = 3.1622<\/p>\n<p><strong>USING THE PYTHAGOREAN THEOREM<\/strong> Approximate the distance between the points to the nearest tenth.<br \/>\nQuestion 37.<br \/>\n(1, 2), (7, 6)<\/p>\n<p>Answer:<br \/>\n7.2 units.<\/p>\n<p>Question 38.<br \/>\n(2, 4), (7, 2)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n(- 1, &#8211; 3), (1, 3)<\/p>\n<p>Answer:<br \/>\n6.3 units.<\/p>\n<p>Question 40.<br \/>\n(- 6, &#8211; 7), (0, 0)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n(- 1, 1), (7, 4)<\/p>\n<p>Answer:<br \/>\n8.5 units.<\/p>\n<p>Explanation:<br \/>\n7 + 1 = 8<br \/>\n4 + 1 = 5<br \/>\n8.5 units<\/p>\n<p>Question 42.<br \/>\n(- 6, 5), (- 4, &#8211; 6)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe locations of several sites in a forest are shown in the coordinate plane. Approximate each distance to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 11\" width=\"289\" height=\"299\" \/><br \/>\na. How far is the cabin from the peak?<br \/>\nb. How far is the fire tower from the lake?<br \/>\nc. How far is the lake from the peak?<br \/>\nd. You are standing at(- 5, &#8211; 6). How far are you from the lake?<\/p>\n<p>Answer:<br \/>\na. 5.8 km<br \/>\nb. 8.6 km<br \/>\nc. 7.1 km<br \/>\nd. 11.7 km<\/p>\n<p>Question 44.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to continue the method in Example 2 to approximate \u221a71 to the nearest hundredth.<\/p>\n<p>Answer:<br \/>\n29<\/p>\n<p>Question 45.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe area of a four square court is 66 square feet. Approximate the side length s of the four square court to the nearest whole number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 12\" width=\"312\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-12.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-12-300x138.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Answer:<br \/>\nThe side length = 8 ft<\/p>\n<p>Explanation:<br \/>\nThe area of a four square court is 66 square feet given.<br \/>\nthe side lengths = 8 x 8<br \/>\ns = 8 ft<\/p>\n<p>Question 46.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA checker board is 8 squares long and 8 squares wide. The area of each square is 14 square centimeters. Approximate the perimeter (in centimeters) of the checker board to the nearest tenth.<\/p>\n<p>Answer:<br \/>\nThe perimeter of the checker board = 384<\/p>\n<p>Explanation:<br \/>\nGiven that the checker board is 8 squares long and 8 squares wide.<br \/>\nperimeter = 6 x side x side<br \/>\nperimeter = 6 x 8 x 8<br \/>\np= 6 x 64<br \/>\np = 384\u00a0 cm<\/p>\n<p>Question 47.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe cube has a volume of 340 cubic inches. Approximate the length d of the diagonal to the nearest whole number. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 13\" width=\"156\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\nThe length of the diagonal = 12 in<\/p>\n<p>Explanation:<br \/>\nGiven that the volume of cube = 340 cubic inches.<br \/>\nv = s x s<br \/>\nv =\u00a0 7 x 7<br \/>\nd = 7 x 7 + 10 x 10 = 149<br \/>\n12 in<br \/>\nQuestion 48.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nOna number line, \u03c0 is between 3 and 4.<br \/>\na. Use this information to draw a number line and shade a region that represents the location of \u03c0<sup>2<\/sup>. Explain your reasoning.<br \/>\nb. Repeat part(a) using the fact that \u03c0 is between 3.1 and 3.<br \/>\nc. Repeat part(a) using the fact that \u03c0 is between 3.14 and 3.15.<br \/>\nAnswer:<\/p>\n<p><strong>NUMBER SENSE<\/strong> Approximate the square root to the nearest tenth.<br \/>\nQuestion 49.<br \/>\n\u221a0.39<\/p>\n<p>Answer:<br \/>\n0.6<\/p>\n<p>Explanation:<br \/>\n\u221a0.39\u00b2<br \/>\nwhere square and square root get cancelled.<br \/>\n0.39\u00a0 &#8211; 10<br \/>\n0.6<\/p>\n<p>Question 50.<br \/>\n\u221a1.19<\/p>\n<p>Answer:<br \/>\n1.09<\/p>\n<p>Explanation:<br \/>\n\u221a1.19\u00b2<br \/>\nwhere square and square root get cancelled.<br \/>\n1.19\u00a0 &#8211; 10<br \/>\n1.09<\/p>\n<p>Question 51.<br \/>\n\u221a1.52<\/p>\n<p>Answer:<br \/>\n1.2<\/p>\n<p>Explanation:<br \/>\n\u221a1.52\u00b2<br \/>\nwhere square and square root get cancelled.<br \/>\n1.52\u00a0 &#8211; 10<br \/>\n1.2<\/p>\n<p>Question 52.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nIs \\(\\sqrt{\\frac{1}{4}}\\) a rational number? Is \\(\\sqrt{\\frac{3}{16}}\\) a rational number? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe equation s<sup>2<\/sup> = 54r represents the relationship between the speed s (in meters per second) of a roller-coaster car and the radius r (in meters) of the loop. Approximate the speed of a roller-coaster car going around the loop shown to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 14\" width=\"186\" height=\"241\" \/><\/p>\n<p>Answer:<br \/>\ns = 30.1 meters per second.<\/p>\n<p>Explanation:<br \/>\ns<sup>2<\/sup> = 54r<br \/>\nwhere r = 16.764 m<br \/>\ns\u00b2 = 54 x 16.764 m<br \/>\ns\u00b2 = 905.256<br \/>\ns =30.1<\/p>\n<p>Question 54.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nFind two numbers a and b that satisfy the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-15.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 15\" width=\"299\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n\u221aa = 9.3<br \/>\n\u221ab = 9.8<\/p>\n<p>Explanation:<br \/>\nGiven that a = 9<br \/>\nb = 10<br \/>\n\u221aa = 9.3<br \/>\n\u221ab = 9.8<br \/>\nthe distance between the two points is 1 inch<\/p>\n<p>Question 55.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe equation d<sup>3<\/sup> = t<sup>3<\/sup> represents the relationship between the mean distance d (in astronomical units) of a planet from the Sun and the t time (in years) it takes the planet to orbit the Sun.<br \/>\na. Jupiter takes about 11.9 years to orbit the Sun. Approximate the mean distance of Jupiter from the Sun to the nearest tenth.<br \/>\nb. The mean distance of Saturn from the Sun is about 9.5 astronomical units. Approximate the time it takes Saturn to orbit the Sun to the nearest tenth.<\/p>\n<p>Answer:<br \/>\na. d = 5.2 astronomical units<br \/>\nb. 29.3 years<\/p>\n<p>Explanation:<br \/>\nGiven that the<br \/>\na. Jupiter takes about 11.9 years to orbit the sun.<br \/>\nb. the mean distance of Saturn from the sun is about 9.5 astronomical units.<br \/>\n<span style=\"font-size: 16px;\">Question 56.<\/span><\/p>\n<p><strong>MODELING REAL LIFE<\/strong><br \/>\nThe equation h = &#8211; 16t<sup>2<\/sup> + 26 represents the height h (in feet) of a water balloon t seconds after it is dropped. Approximate the time it takes the water balloon to reach the ground to the nearest tenth. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.5-16.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem 9.5 16\" width=\"185\" height=\"202\" \/><\/p>\n<p>Answer:<br \/>\n&#8211; 28 feet.<\/p>\n<p>Explanation:<br \/>\nGiven that the equation h = &#8211; 16t<sup>2<\/sup> + 26<br \/>\nwe assuming t = 2<br \/>\nh = -16 x 4 + 26<br \/>\nh = -64 + 26<br \/>\nh = -38<br \/>\nnearest tenth = 38 &#8211; 10<br \/>\n&#8211; 28 feet<\/p>\n<p>Question 57.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nDetermine whether the statement is sometimes, always, or never true. Explain your reasoning.<br \/>\na. A rational number multiplied by a rational number is rational.<br \/>\nb. A rational number multiplied by an irrational number is rational.<br \/>\nc. An irrational number multiplied by an irrational number is rational.<\/p>\n<p>Answer:<br \/>\na. always.<br \/>\nb. sometimes.<br \/>\nc. sometimes.<\/p>\n<p>Explanation:<br \/>\na. if a\/b and c\/d are rational numbers, then ac and bd are integers and bd not equal to zero. so ac\/bd is rational.<br \/>\nb. for example, \u03c0 . 0 = 0 is rational, but 2. \u221a3 is irrational.<br \/>\nc. for example, \u221a2 . \u03c0\u00a0 is irrational, but \u03c0\u00a0 . 1\/ \u03c0\u00a0 is rational.<\/p>\n<h3><a id=\"Lesson_9.6_The_Converse_of_the_Pythagorean_Theorem\"><\/a>Lesson 9.6 The Converse of the Pythagorean Theorem<\/h3>\n<p><strong>The converse of a statement switches the hypothesis and the conclusion.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 1\" width=\"362\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-1.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-1-300x61.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Analyzing the Converse of a Statement<br \/>\nWork with a partner.<br \/>\na.Write the converse of each statement. Then determine whether each statement and its converse are true or false.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 2\" width=\"136\" height=\"141\" \/><\/p>\n<ul>\n<li>If I live in California,then I live in the United States.<\/li>\n<li>If my heart is beating, then I am alive.<\/li>\n<li>If one figure is a translation of another figure,then the figures are congruent.<\/li>\n<\/ul>\n<p>b. Write your own statement whose converse is true. \ue01den write your own statement whose converse is false.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>The Converse of the Pythagorean Theorem<br \/>\nWork with a partner.<br \/>\na.Write the converse of the Pythagorean Theorem. Do you think the converse is true or false?<br \/>\nb. Consider \u25b3DEFwith side lengths a, b, and c such that a<sup>2<\/sup> + b<sup>2<\/sup> = c<sup>2<\/sup>. Also consider \u25b3JKL with leg lengths a and b, where the measure of \u2220K is 90\u00b0. Use the two triangles and the Pythagorean Theorem to show that the converse of the Pythagorean Theorem is true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 3\" width=\"415\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-3.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-3-300x117.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether the triangle with the given side lengths is a right triangle.<\/strong><br \/>\nQuestion 1.<br \/>\n28 in., 21 in., 20 in.<\/p>\n<p>Answer:<br \/>\nThe given sides does not form a right triangle.<br \/>\nExplanation:<br \/>\n20\u00b2 + 21\u00b2 = 28\u00b2<br \/>\n400\u00a0 + 441 = 784<br \/>\n841 = 784<br \/>\nthe given sides does not form a right triangle.<\/p>\n<p>Question 2.<br \/>\n1.25 mm, 1 mm, 0.75 mm<\/p>\n<p>Answer:<br \/>\nThe given sides form a right triangle.<br \/>\nExplanation:<br \/>\n1\u00b2 + 0.75\u00b2 = 1.25\u00b2<br \/>\n1 + 0.5625= 1.5623<br \/>\n1.5625 = 784<br \/>\nthe given sides\u00a0 form a right triangle.<\/p>\n<p><strong>Tell whether the points form a right triangle.<\/strong><br \/>\nQuestion 4.<br \/>\nD (- 4, 0), E (- 2, 3), F (1, 0)<\/p>\n<p>Answer:<br \/>\nYes the given points form a right triangle.<\/p>\n<p>Question 5.<br \/>\nJ (4, 1), K (1, &#8211; 3), L (- 3, 0)<\/p>\n<p>Answer:<br \/>\nYes the given points form a right triangle.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain the converse of the Pythagorean Theorem.<\/p>\n<p>Answer:<br \/>\na\u00b2 + b\u00b2 \u2260 c\u00b2<\/p>\n<p>Explanation:<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\nwhere a, b and c are side lengths of a triangle.<br \/>\nconverse of pythagoras theorem<br \/>\na\u00b2 + b\u00b2 \u2260 c\u00b2<\/p>\n<p>Question 6.<br \/>\n<strong>IDENTIFYING A RIGHT TRIANGLE<\/strong><br \/>\nIs a triangle with side lengths of 2 millimeters, 2.5 millimeters, and 3 millimeters a right triangle?<\/p>\n<p>Answer:<br \/>\nNo the side lengths does not form a right triangle.<\/p>\n<p>Explanation:<br \/>\n2 \u00b2 + 2.5\u00b2 = 3\u00b2<br \/>\n4\u00a0 + 6.25 = 9<br \/>\n10.25 = 9<\/p>\n<p>Question 7.<br \/>\n<strong>IDENTIFYING A RIGHT TRIANGLE<\/strong><br \/>\nDo the points (- 1, 1), (- 3, 5), and (0, 8) form a right triangle?<\/p>\n<p>Answer:<br \/>\nNo the given points does not form a right triangle.<\/p>\n<p>Question 8.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich set of numbers does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-4.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 4\" width=\"348\" height=\"40\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-4.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-4-300x34.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Answer:<br \/>\n3, 6, 8 set does not belong with the other 3 sets.<\/p>\n<p>Explanation:<br \/>\n3 \u00b2 + 6\u00b2 = 8\u00b2<br \/>\n9\u00a0 + 36 = 64<br \/>\n45 = 64<br \/>\nthe given sides does not form a right triangle.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nYou practice archery as shown. Determine whether the arrow is perpendicular to the vertical support. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-5.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 5\" width=\"136\" height=\"204\" \/><\/p>\n<p>Answer:<br \/>\nYes the archery is perpendicular to vertical support.<\/p>\n<p>Explanation:<br \/>\n2 times of 7 is 14.<br \/>\nso archery is perpendicular to vertical support.<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThree fire hydrants in a neighborhood are represented on a map. The coordinates of the fire hydrants are (0, 0), (2, 5), and (7, y). The fire hydrants are arranged in a right triangle, where y is a natural number less than 10. Find y.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-6.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 6\" width=\"110\" height=\"169\" \/><\/p>\n<p>Answer:<br \/>\ny = 5<\/p>\n<p>Explanation:<br \/>\nGiven that the coordinates of the fire hydrants are (0, 0), (2, 5), and (7, y).<br \/>\ny can meet the y-axis on 5<br \/>\ny = 5<br \/>\n7 -2 = 5<\/p>\n<h3><a id=\"The_Converse_of_the_Pythagorean_Theorem_Homework_&amp;_Practice_9.6\"><\/a>The Converse of the Pythagorean Theorem Homework &amp; Practice 9.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Approximate the number to the nearest (a) integer and (b) tenth.<\/strong><br \/>\nQuestion 1.<br \/>\n\u221a31<\/p>\n<p>Answer:<br \/>\na. 6<br \/>\nb. 5.6<\/p>\n<p>Explanation:<br \/>\nsquare root of 31 = 31<br \/>\n\u221a31 \u00b2 = 6<br \/>\nwhere square and square root get cancelled.<br \/>\nnearest tenth = it is decreased by 10<br \/>\n5.6<\/p>\n<p>Question 2.<br \/>\n&#8211; \u221a7<\/p>\n<p>Answer:<br \/>\na. 7<br \/>\nb. -3<\/p>\n<p>Explanation:<br \/>\nsquare root of 7 = 7<br \/>\n\u221a7 \u00b2 = 7<br \/>\nwhere square and square root get cancelled.<br \/>\nnearest tenth = it is decreased by 10<br \/>\n7 -10<br \/>\n-3<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt [ 3 ]{ 25 }\\)<\/p>\n<p>Answer:<br \/>\na. 3<br \/>\nb. 2.9<\/p>\n<p>Explanation:<br \/>\ncube root of 25 = 25<br \/>\n3\u221a25 = 3<br \/>\nwhere square and square root get cancelled.<br \/>\nnearest tenth = it is decreased by 10<br \/>\n2.9<\/p>\n<p><strong>The figures are similar. Find x.<\/strong><br \/>\nQuestion 4.<br \/>\nThe ratio of the perimeters is 2 : 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-7.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 7\" width=\"197\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\nx = 2<\/p>\n<p>Explanation:<br \/>\nGiven that the ratio of perimeters = 2 : 5<br \/>\nx = 2<br \/>\n5 x 2 = 10<\/p>\n<p>Question 5.<br \/>\nThe ratio of the perimeters is 4 : 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-8.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 8\" width=\"163\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nx = 4.5<\/p>\n<p>Explanation:<br \/>\nGiven that the ratio of perimeters = 4 : 3<br \/>\nx = 4.5<br \/>\n3 x 2 = 4.5<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>ANALYZING THE CONVERSE OF A STATEMENT<\/strong> Write the converse of the statement. Then determine whether the statement and its converse are true or false. Explain. (See Exploration 1, p. 409.)<br \/>\nQuestion 6.<br \/>\nIf a is an odd number, then a<sup>2<\/sup> is odd.<\/p>\n<p>Answer:<br \/>\nFalse.<br \/>\nif a is not an odd number, then square of a is not odd.<\/p>\n<p>Explanation:<br \/>\nThe given statement is true.<br \/>\nconverse of a given statement is false.<\/p>\n<p>Question 7.<br \/>\nIf ABCD is a square, then ABCD is a parallelogram.<\/p>\n<p>Answer:<br \/>\nTrue.<br \/>\nIf ABCD is\u00a0 not a square, then ABCD is not a parallelogram.<\/p>\n<p>Explanation:<br \/>\nThe given statement is false.<br \/>\nconverse of a given statement is true.<br \/>\n<strong>IDENTIFYING A RIGHT TRIANGLE<\/strong> Tell whether the triangle with the given side lengths is a right triangle.<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-9.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 9\" width=\"150\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\nYes the given side lengths is a right triangle.<\/p>\n<p>Explanation:<br \/>\n8 \u00b2 + 15\u00b2 = 17\u00b2<br \/>\n64\u00a0 + 225 = 289<br \/>\n289 = 625<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-10.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 10\" width=\"159\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nYes the given side lengths is a right triangle.<\/p>\n<p>Explanation:<br \/>\n27 \u00b2 + 36\u00b2 = 45\u00b2<br \/>\n729\u00a0 + 1296 = 2025<br \/>\n2025 = 625<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-11.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 11\" width=\"158\" height=\"104\" \/><\/p>\n<p>Answer:c<\/p>\n<p><span style=\"font-size: 16px;\">Question 11.<\/span><\/p>\n<p>14 mm, 19 mm, 23 mm<\/p>\n<p>Answer:<br \/>\nNo the given side lengths is not a right triangle.<\/p>\n<p>Explanation:<br \/>\n14 \u00b2 + 19\u00b2 = 23\u00b2<br \/>\n196\u00a0 + 361\u00a0 = 529<br \/>\n557 = 625<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{9}{10}\\) mi, 1 \\(\\frac{1}{5}\\) mi, 1 \\(\\frac{1}{2}\\) mi<\/p>\n<p>Answer:<\/p>\n<p>Question 13.<br \/>\n1.4 m, 4.8 m, 5 m<\/p>\n<p>Answer:<br \/>\nYes the given side lengths is\u00a0 a right triangle.<\/p>\n<p>Explanation:<br \/>\n1.4 \u00b2 + 4.8\u00b2 = 5\u00b2<br \/>\n1.96\u00a0 + 23.04\u00a0 = 25<br \/>\n25 = 25<\/p>\n<p>Question 14.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA post-and-beam frame for a shed is shown in the diagram. Does the brace form a right triangle with the post and beam? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-12.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 12\" width=\"193\" height=\"197\" \/><\/p>\n<p>Answer:<br \/>\nYes the given side lengths is a right triangle.<\/p>\n<p>Explanation:<br \/>\n15 \u00b2 + 20\u00b2 = 25\u00b2<br \/>\n225\u00a0 + 400 = 625<br \/>\n625 = 625<\/p>\n<p>Question 15.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA traffic sign has side lengths of 12.6 inches, 12.6 inches, and 12.6 inches. Is the sign a right triangle? Explain.<\/p>\n<p>Answer:<br \/>\nNo the given side lengths is not a right triangle.<\/p>\n<p>Explanation:<br \/>\n12.6 \u00b2 + 12.6\u00b2 = 12.6\u00b2<br \/>\n158.76 + 158.76 = 158.76<br \/>\n317.52 = 158.76<\/p>\n<p><strong>IDENTIFYING A RIGHT TRIANGLE<\/strong> Tell whether a triangle with the given side lengths is a right triangle.<br \/>\nQuestion 16.<br \/>\n\u221a63, 9, 12<\/p>\n<p>Answer:<br \/>\nYes the given side lengths is a right triangle.<\/p>\n<p>Explanation:<br \/>\n\u221a63 \u00b2 + 9\u00b2 = 12\u00b2<br \/>\n63 + 81 = 144<br \/>\n144 = 144<\/p>\n<p>Question 17.<br \/>\n4, \u221a15, 6<\/p>\n<p>Answer:<br \/>\nNo the given side lengths is not a right triangle.<\/p>\n<p>Explanation:<br \/>\n\u221a15 \u00b2 + 4\u00b2 = 6\u00b2<br \/>\n15 + 16 = 36<br \/>\n31 = 36<\/p>\n<p>Question 18.<br \/>\n\u221a18, \u221a24, \u221a42<\/p>\n<p>Answer:<br \/>\nYes the given side lengths is a right triangle.<\/p>\n<p>Explanation:<br \/>\n\u221a18 \u00b2 + \u221a24\u00b2 = \u221a42\u00b2<br \/>\n18 +24 = 42<br \/>\n42= 42<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend determines whether a triangle with side lengths of 3, \u221a58, and 7 is a right triangle. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-13.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 13\" width=\"252\" height=\"152\" \/><\/p>\n<p>Answer:<br \/>\nNo my friend is\u00a0 not correct.<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n13\u00b2 + 58\u00b2 = 7\u00b2<br \/>\n9 + 58\u00a0 is not equal to 49<\/p>\n<p><strong>IDENTIFYING A RIGHT TRIANGLE<\/strong> Tell whether the points form a right triangle.<br \/>\nQuestion 20.<br \/>\n(0, 0), (0, 5), (2, 0)<\/p>\n<p>Answer:<br \/>\nYes the points\u00a0 forms a right triangle<\/p>\n<p>Explanation:<br \/>\nthe above given points are all positive<\/p>\n<p><span style=\"font-size: 16px;\">Question 21.<\/span><\/p>\n<p>(0, 8), (2, 2), (11, 6)<\/p>\n<p>Answer:<br \/>\nNo the points not forms a right triangle<\/p>\n<p>Explanation:<br \/>\nthe above given points are all positive.<\/p>\n<p>Question 22.<br \/>\n(- 1, 0), (5, 0), (2, &#8211; 3)<\/p>\n<p>Answer:<br \/>\nNo the points not forms a right triangle<\/p>\n<p>Explanation:<br \/>\nthe above given points are all positive and negative.<\/p>\n<p>Question 23.<br \/>\n(- 1, &#8211; 2), (2, 6), (4, &#8211; 1)<\/p>\n<p>Answer:<br \/>\nNo the points does not forms a right triangle<\/p>\n<p>Explanation:<br \/>\nthe above given points are all positive<\/p>\n<p><span style=\"font-size: 16px;\">Question 24.<\/span><\/p>\n<p><span style=\"font-size: 16px;\">(- 8, 6), (7, 9), (0, &#8211; 13)<\/span><\/p>\n<p>Answer:<br \/>\nYes the points\u00a0 forms a right triangle<\/p>\n<p>Explanation:<br \/>\nthe above given points are all positive and negative<\/p>\n<p>Question 25.<br \/>\n(0.5, 1.5), (7.5, 5.5), (9.5, 0.5)<\/p>\n<p>Answer:<br \/>\nNo\u00a0 the points does not\u00a0 forms a right triangle<\/p>\n<p>Explanation:<br \/>\nthe above given points are all positive and negative<\/p>\n<p>Question 26.<br \/>\n<strong>LOGIC<\/strong><br \/>\nThe equation a<sup>2<\/sup> + b<sup>2<\/sup> = c<sup>2<\/sup> is not true for a particular triangle with side lengths of a, b, and c. What can you conclude about the type of triangle?<\/p>\n<p>Answer:<br \/>\nIf the triangle is right triangle the above condition satisfies.<\/p>\n<p>Explanation:<br \/>\nThe equation\u00a0a<sup>2<\/sup> + b<sup>2<\/sup> = c<sup>2<\/sup>\u00a0is a pythagoras theroem.<br \/>\nit satisfies for only right triangle.<br \/>\nwhere a,b, c are side lengths.<br \/>\nQuestion 27.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou spend the day looking for hidden containers in a wooded area using a Global Positioning System (GPS). You park your bike on the side of the road, and then locate Container 1 and Container 2 before going back to your bike. Does your path form a right triangle? Explain. Each grid line represents 10 yards.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-14.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 14\" width=\"198\" height=\"169\" \/><\/p>\n<p>Answer:<br \/>\nNo path does not forms a right triangle.<\/p>\n<p>Explanation:<br \/>\n(10, 50) , (20, -20) and (80, -10)<br \/>\nthe given points form a right triangle.<\/p>\n<p>Question 28.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe locations of a fishing boat, buoy, and kayak are represented by the points (0, 0), (16, 12), and (10, &#8211; 5). Each unit represents 1 nautical mile<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-9.6-15.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 9 Real Numbers and the Pythagorean Theorem 9.6 15\" width=\"272\" height=\"201\" \/><br \/>\na. Do the boat, kayak, and buoy form a right triangle?<br \/>\nb. The boattravels at8 nautical miles per hour. How long does the boat take to reach the buoy if the boat travels directly toward it?<\/p>\n<p>Answer:<br \/>\na. yes the boat, kayak, buoy form a right triangle.<br \/>\nb. the boat travels at 8 nautical miles per hr= 80 miles per hr<\/p>\n<p>Explanation:<br \/>\na.yes the boat, kayak, buoy form a right triangle.<br \/>\nb. the boat travels at 8 nautical miles per hr.<br \/>\n8 x 10<br \/>\n80 miles per hr<\/p>\n<p>Question 29.<br \/>\nThe vertices of a quadrilateral are (1, 2), (5, 4), (6, 2), and (2, 0). Use the converse of the Pythagorean Theorem to determine whether the quadrilateral is a rectangle.<br \/>\nAnswer:<br \/>\nYes the given points forms a rectangle.<\/p>\n<h3><a id=\"Real_Numbers_and_the_Pythagorean_Theorem_Connecting_Concepts\"><\/a>Real Numbers and the Pythagorean Theorem Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nThe scale drawing of a baseball field has a scale factor of \\(\\frac{1}{270}\\). Approximate the distance from home plate to second base on the actual baseball field to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cc-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cc 1\" width=\"280\" height=\"264\" \/><br \/>\nUnderstand the problem.<br \/>\nYou know several measurements and the scale factor in a scale drawing of a baseball field. You are asked to approximate the distance from home plate to second base on the actual baseball field.<\/p>\n<p>Make a plan.<br \/>\nThe distance from home plate to second base is the hypotenuse of a right triangle. Approximate the distance in the scale drawing to the nearest tenth. Then use the scale factor to approximate the distance on the actual field.<\/p>\n<p>Solve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<br \/>\n0.048 sq in<\/p>\n<p>Explanation:<br \/>\nGiven that the scale factor of (1\/270)<br \/>\n(1\/270) = 0.003<br \/>\nfrom home plate to second base<br \/>\n4 x 4<br \/>\n16 x 0.003<br \/>\n0.048<\/p>\n<p>Question 2.<br \/>\nYou cut the wood cube shown into two identical triangular prisms. Approximate the surface area of each triangular prism to the nearest tenth. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cc-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cc 2\" width=\"149\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nThe surface area of triangular prism = 64 cm<\/p>\n<p>Explanation:<br \/>\nthe volume of the cube<br \/>\nv = s x s x<br \/>\nv = 8 x 8 x 8<br \/>\nv = 64 x 8<br \/>\nv = 512<\/p>\n<p>Question 3.<br \/>\nComplete the mapping diagram representing the relationship between the lengths of the hypotenuse and the legs of an isosceles right triangle. Is the relationship linear? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cc-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cc 3\" width=\"197\" height=\"159\" \/><\/p>\n<p>Answer:<br \/>\na\u221a2<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Identify and Correct the Error!<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cMetronome Design.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cc-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cc 4\" width=\"348\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cc-4.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cc-4-300x154.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Answer:<\/p>\n<h3><a id=\" Real_Numbers_and_the_Pythagorean_Theorem_Chapter_Review\"><\/a>Real Numbers and the Pythagorean Theorem Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 1\" width=\"559\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-1.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-1-300x44.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nYou can use a Four Square to organize information about a concept. Each of the four squares can be a category, such as definition, vocabulary, example, non-example, words, algebra, table, numbers, visual, graph, or equation. Here is an example of a Four Square for Pythagorean Theorem.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 2\" width=\"478\" height=\"324\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-2.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-2-300x203.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 3\" width=\"289\" height=\"282\" \/><br \/>\n1. square roots<br \/>\n2. cube roots<br \/>\n3. rational numbers<br \/>\n4. irrational numbers<br \/>\n5. real numbers<br \/>\n6. converse of the Pythagorean Theorem<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 4\" width=\"597\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-4.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-4-300x37.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p><strong>9.1 Finding Square Roots (pp. 373\u2013380)<\/strong><br \/>\nLearning Target: Understand the concept of a square root of a number.<\/p>\n<p><strong>Find the square root(s).<\/strong><br \/>\nQuestion 1.<br \/>\n\u221a1<\/p>\n<p>Answer:<br \/>\n1<\/p>\n<p>Explanation:<br \/>\nsquare root of 1 = 1 x 1<\/p>\n<p>Question 2.<br \/>\n&#8211; \\(\\sqrt{\\frac{9}{25}}\\)<\/p>\n<p>Answer:<br \/>\n-(3\/5)<\/p>\n<p>Explanation:<br \/>\nsquare root of 9 = 3x 3<br \/>\nsquare root of 25 = 5 x 5<\/p>\n<p>Question 3.<br \/>\n\u00b1 \u221a1.69<\/p>\n<p>Answer:<br \/>\n\u00b1 1.3<\/p>\n<p>Explanation:<br \/>\nsquare root of 1.69 = 1.3 x 1.3<\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 4.<br \/>\n15 &#8211; 4 \u221a36<\/p>\n<p>Answer:<br \/>\n-9<\/p>\n<p>Explanation:<br \/>\n15 &#8211; 4 \u221a36<br \/>\nsquare root of 36 = 6 x 6<br \/>\n15 &#8211; 4 x 6<br \/>\n15 &#8211; 24<br \/>\n-9<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt{\\frac{54}{6}}+\\frac{2}{3}\\)<\/p>\n<p>Answer:<br \/>\n9.66<\/p>\n<p>Explanation:<br \/>\n(54\/6) = 9<br \/>\n(2\/3) = 0.66<br \/>\n9 + 0.66<br \/>\n9.66<\/p>\n<p>Question 6.<br \/>\n\\((\\sqrt{9})^{2}\\) &#8211; 12<\/p>\n<p>Answer:<br \/>\n-7.5<\/p>\n<p>Explanation:<br \/>\n(9\/2) = 4.5<br \/>\n4.5 &#8211; 12<br \/>\n-7.5<\/p>\n<p>Question 7.<br \/>\nThe total area of a checker board is 256 square inches. What is the side length (in inches) of one of the small squares?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 7\" width=\"137\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nThe side length = 16 in<\/p>\n<p>Explanation:<br \/>\nGiven that total area = 256 sq in<br \/>\narea of square = s x s<br \/>\narea = 16 x 16<br \/>\nside = 16 in<\/p>\n<p><strong>9.2 The Pythagorean Theorem (pp. 381\u2013388)<\/strong><br \/>\nLearning Target: Understand the Pythagorean Theorem.<\/p>\n<p><strong>Find the missing length of the triangle.<\/strong><br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 8\" width=\"229\" height=\"90\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 47 in<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n12\u00b2 + 35\u00b2 = 47\u00b2<br \/>\nlength = 47 in<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-9.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 9\" width=\"195\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 0.2 cm<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n0.3\u00b2 + 0.2\u00b2 = 0.5\u00b2<br \/>\nlength = 0.2 cm<\/p>\n<p>Question 10.<br \/>\nYou lean a 13-foot ladder on a house so the bottom of the ladder is 5 feet from the house. From the top of the ladder, you can safely reach another 4 feet higher. Can you reach a window that is located 13 feet above the ground? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-10.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 10\" width=\"132\" height=\"205\" \/><\/p>\n<p>Answer:<br \/>\nNo we cannot reach a window.<\/p>\n<p>Explanation:<br \/>\nGiven that we lean a 13-foot ladder on a house<br \/>\nso that the bottom of the ladder is 5 feetfrom the house.<br \/>\nfrom the top of ladder, we can reach safely another 4 feet higher.<br \/>\n5 + 4<br \/>\nwe can reach 9 feet.<\/p>\n<p>Question 11.<br \/>\nFind the distance between (- 6, 8) and (10, &#8211; 4).<br \/>\nAnswer:<\/p>\n<p><strong>9.3 FindingCube Roots (pp. 389\u2013394)<\/strong><br \/>\nLearning Target: Understand the concept of a cube root of a number.<\/p>\n<p><strong>Find the cube root.<\/strong><br \/>\nQuestion 12.<br \/>\n\\(\\sqrt [ 3 ]{ -2197 }\\)<\/p>\n<p>Answer:<br \/>\n-13<\/p>\n<p>Explanation:<br \/>\ncube root of (-2197) is (-13)<br \/>\n3\u221a-2197= (-13) x (-13) x (-13)<br \/>\n-2197\u00b3 = (-13)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n-2197 = -13<\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt[3]{\\frac{64}{343}}\\)<\/p>\n<p>Answer:-<br \/>\n(4\/7)<\/p>\n<p>Explanation:<br \/>\ncube root of (64\/343) is (4\/7)<br \/>\n3\u221a(64\/343)= (4\/7) x (4\/7) x (4\/7)<br \/>\n(64\/343)\u00b3 = (4\/7)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n(64\/343)= (4\/7)<\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt[3]{-\\frac{8}{27}}\\)<\/p>\n<p>Answer:<br \/>\n-2\/3<\/p>\n<p>Explanation:<br \/>\ncube root of (8\/27) is (2\/3)<br \/>\n3\u221a(8\/27)= (2\/3) x (2\/3) x (2\/3)<br \/>\n(8\/27)\u00b3 = (2\/3)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n(8\/27)= (2\/3)<\/p>\n<p>Question 15.<br \/>\nEvaluate the expression 25 + 2\\(\\sqrt [ 3 ]{ -64 }\\).<br \/>\nAnswer:<br \/>\n17<\/p>\n<p>Explanation:<br \/>\ncube root of (-64) is (-4)<br \/>\n3\u221a(64)= (4) x (4) x (4)<br \/>\n(64)\u00b3 = (4)\u00b3<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n(64)= 4<br \/>\n25 + 2(-4)<br \/>\n25 -8<br \/>\n17<\/p>\n<p>Question 16.<br \/>\nSolve the equation &#8211; 55 = \\(\\frac{1}{4}\\)x<sup>3<\/sup> + 73.<br \/>\nAnswer:<br \/>\nx =8<\/p>\n<p>Explanation:<br \/>\n-55 = 0.25 x \u00b3 + 73<br \/>\n0.25 x\u00b3 = -55 -73<br \/>\n0.25 x\u00b3 = -128<br \/>\nx\u00b3 = -(128\/0.25)<br \/>\nx\u00b3 = 512<br \/>\nx = 8<\/p>\n<p>Question 17.<br \/>\nYou are shipping a puzzle cube to your friend using the cube-shaped box shown. What is the difference between the height of the puzzle cube and the top of the box when you place the cube in the box?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-17.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 17\" width=\"288\" height=\"164\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the puzzle cube = 6 cm<\/p>\n<p>Explanation:<br \/>\nGiven that the volume of the cube-shaped box = 216 cubic cm<br \/>\nvolume of cube = s x s x s<br \/>\nv = 6 x 6 x 6<br \/>\nv = 36 x 6<br \/>\nv = 216<br \/>\nthe height of puzzle cube= 6 cm<\/p>\n<p><strong>9.4 Rational Numbers (pp. 395\u2013400)<\/strong><br \/>\nLearning Target: Convert between different forms of rational numbers.<\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><br \/>\nQuestion 18.<br \/>\n&#8211; 2\\(\\frac{5}{6}\\)<\/p>\n<p>Answer:<br \/>\n-1.66<\/p>\n<p>Explanation:<br \/>\n(5\/6) = 0.83<br \/>\n-1.66<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{27}{80}\\)<\/p>\n<p>Answer:<br \/>\n0.33<\/p>\n<p>Explanation:<br \/>\n(27\/80)<br \/>\n0.3375<\/p>\n<p>Question 20.<br \/>\n3\\(\\frac{8}{9}\\)<\/p>\n<p>Answer:<br \/>\n2.66<\/p>\n<p>Explanation:<br \/>\n(8\/9)\u00a0 = 0.888<br \/>\n3 x 8\/9<br \/>\n3 x 0.88<br \/>\n2.66<\/p>\n<p>Question 21.<br \/>\nWrite \\(1 . \\overline{36}\\) as a mixed number.<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\nThe gas mileage of a hybrid car is \\(3.0 \\overline{3}\\) times the gas mileage of a regular car. The regular car averages 24 miles per gallon. Find the gas mileage of the hybrid car.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-22.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 22\" width=\"328\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-22.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-22-300x115.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<br \/>\nThe gas mileage of the hybrid car is 72 miles<\/p>\n<p>Explanation:<br \/>\nGiven that the mileage of the hybrid car is 3<br \/>\nthe regular car averages 24 miles per gallon.<br \/>\nthe gas mileage of the hybrid car is<br \/>\n24 x 3<br \/>\n72 miles<\/p>\n<p>Question 23.<br \/>\nYour friend\u2019s cat weighs 0.8 3 times the weight of your cat. Your friend\u2019s cat weighs 10 pounds. How much more does your cat weigh than your friend\u2019s cat?<\/p>\n<p>Answer:<br \/>\n2 pounds<\/p>\n<p>Explanation:<br \/>\nGiven that the my friend&#8217;s cat weighs = 0.8<br \/>\n3 times the weight of my cat.<br \/>\nmy friend cat weighs = 10 pounds<br \/>\n10 x 0.2 = 2 pounds.<\/p>\n<p>Question 23.<br \/>\nAn apple dessert recipe makes \\(2 . \\overline{3}\\) pounds of dessert and serves 6 people. What is the serving size (in pounds)?<\/p>\n<p>Answer:<br \/>\nThe serving size is 18 pounds.<\/p>\n<p>Explanation:<br \/>\ngiven that an apple dessert recipe makes 3 pounds.<br \/>\nthe serving size is<br \/>\n6 x 3<br \/>\n18 pounds.<\/p>\n<p><strong>9.5 Irrational Numbers (pp. 401\u2013408)<\/strong><br \/>\nLearning Target: Understand the concept of irrational numbers.<\/p>\n<p><strong>Classify the real number.<\/strong><br \/>\nQuestion 24.<br \/>\n\\(0.81 \\overline{5}\\)<\/p>\n<p>Answer:<br \/>\nreal number<\/p>\n<p>Explanation:<br \/>\ngiven expression is a real number.<\/p>\n<p>Question 25.<br \/>\n\u221a101<br \/>\nAnswer:<br \/>\nno<\/p>\n<p>Explanation:<br \/>\nsquare root of 101 is real algebraic number<br \/>\nso it is not a real number.<\/p>\n<p>Question 26.<br \/>\n\u221a4<br \/>\nAnswer:<br \/>\nno<\/p>\n<p>Explanation:<br \/>\nsquare root of 4 is real algebraic number<br \/>\nso it is not a real number.<\/p>\n<p>Approximate the number to the nearest (a) integer and (b) tenth.<br \/>\nQuestion 27.<br \/>\n\u221a14<\/p>\n<p>Answer:<br \/>\na. 3<br \/>\nb. 4<\/p>\n<p>Explanation:<br \/>\n3 is a integer for square root of 14<br \/>\n4 is the nearest tenth for 14<\/p>\n<p>Question 28.<br \/>\n\u221a90<\/p>\n<p>Answer:<br \/>\n89<br \/>\n80<\/p>\n<p>Explanation:<br \/>\n89 is a integer for square root of 90<br \/>\n80 is the nearest tenth for 90<\/p>\n<p>Question 29.<br \/>\n\u221a175<\/p>\n<p>Answer:<br \/>\n174<br \/>\n165<\/p>\n<p>Explanation:<br \/>\n174 is a integer for square root of 175<br \/>\n165 is the nearest tenth for 175<\/p>\n<p>Question 31.<br \/>\nWhich is greater, \u221a48 or \\(\\sqrt [ 3 ]{ 127 }\\) ? Explain.<\/p>\n<p>Answer:<br \/>\ncube root of 127 is greater.<\/p>\n<p>Explanation:<br \/>\ncube root of 127 = 127<br \/>\ncube root of 48 = 48<\/p>\n<p>Question 32.<br \/>\nApproximate the distance between (- 2, &#8211; 5) and (3, 5) to the nearest tenth.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nThe equation d = \\(\\frac{v^{2}}{15.68}\\)represents the relationship between the distance d (in meters) needed to stop a vehicle and the velocity v (in meters per second) of the vehicle. Approximate the velocity of the vehicle when it takes 40 meters to stop.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-33.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 33\" width=\"181\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nThe velocity of vehicle\u00a0 = 5.102 meters<\/p>\n<p>Explanation:<br \/>\ngiven that the equation d = (2\/15.68)<br \/>\n(2\/15.68 = 0.12755<br \/>\nthe velocity of the vehicle when it takes 40 meters<br \/>\n0.12755 x 40<br \/>\n5.102 meters.<\/p>\n<p><strong>9.6 The Converse of the Pythagorean Theorem (pp. 409\u2013414)<\/strong><br \/>\nLearning Target: Understand the converse of the Pythagorean Theorem.<\/p>\n<p><strong>Tell whether the triangle with the given side lengths is a right triangle.<\/strong><br \/>\nQuestion 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-34.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 34\" width=\"241\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\nyes.<\/p>\n<p>Explanation:<br \/>\nthe given triangle is a right triangle.<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-35.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 35\" width=\"195\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nno<\/p>\n<p>Explanation:<br \/>\nthe given measures not forming a right triangle.<\/p>\n<p>Question 36.<br \/>\nTell whether the points A (1, &#8211; 1), B (3, &#8211; 4), and C (4, 1) form a right triangle.<\/p>\n<p>Answer:<br \/>\nno<\/p>\n<p>Explanation:<br \/>\ngiven that the points<br \/>\nA(1, -1) B(3, -4) and C(4, 1)<br \/>\nthe given measures does not form the right triangle.<\/p>\n<p>Question 37.<br \/>\nYou want to make a wooden border around a flower bed in the shape of a right triangle. You have three pieces of wood that measure 3.5 meters, 1.2 meters, and 3.9 meters. Do these pieces of wood form a right triangle? If not, explain how you can cut the longest piece of wood to make a right triangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cr-37.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cr 37\" width=\"153\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nYes these pieces of wood form a right triangle.<\/p>\n<p>Explanation:<br \/>\nGiven that the length of wooden pieces have measures of 3.5 m, 1.2 m, 3.9 m<br \/>\nso it can cut the wooden border in the shape of right triangle.<\/p>\n<h3><a id=\"Real_Numbers_and_the_Pythagorean_Theorem_Practice_Test\"><\/a>Real Numbers and the Pythagorean Theorem Practice Test<\/h3>\n<p>Question 1.<br \/>\nFind \u2212 \u221a1600 .<\/p>\n<p>Answer:<br \/>\n-40<\/p>\n<p>Explanation:<br \/>\nsquare root of 1600 = 40 x 40<br \/>\n\u221a1600 = 40\u00b2<br \/>\nwhen powers are equal exponents must be equal.<br \/>\n40<\/p>\n<p>Question 2.<br \/>\nFind \\(\\sqrt[3]{-\\frac{729}{64}}\\).<\/p>\n<p>Answer:<br \/>\n(-9\/4)<\/p>\n<p>Explanation:<br \/>\ncube root of -729 = 9<br \/>\ncube root of -64 = 4<br \/>\n-(9\/4)<\/p>\n<p>Evaluate the expression.<br \/>\nQuestion 3.<br \/>\n12 + 8\u221a16<\/p>\n<p>Answer:<br \/>\n80<\/p>\n<p>Explanation:<br \/>\n12 + 8\u221a16<br \/>\nsquare root of 16 is 4<br \/>\n12 + 8 x 4<br \/>\n20 x 4<br \/>\n80<\/p>\n<p>Question 4.<br \/>\n\\((\\sqrt[3]{-125})^{3}+75\\)<\/p>\n<p>Answer:<br \/>\n60<\/p>\n<p>Explanation:<br \/>\ncube root of -125 is -5<br \/>\n-5 x 3 + 75<br \/>\n-15 + 75<br \/>\n60<br \/>\nQuestion 5.<br \/>\nFind the missing length of the triangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-pt-5.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem pt 5\" width=\"253\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nThe missing length = 2 in<\/p>\n<p>Explanation:<br \/>\nBy using Pythagoras theorem<br \/>\na\u00b2 + b\u00b2 = c\u00b2<br \/>\n2\u00b2 + 24\u00b2 = 26\u00b2<br \/>\nlength = 2 in<\/p>\n<p>Classify the real number.<br \/>\nQuestion 6.<br \/>\n16 \u03c0<\/p>\n<p>Answer:<br \/>\n4\u03c0<\/p>\n<p>Explanation:<br \/>\nsquare root of 16 = 4 x 4<br \/>\nsquare root of 16 = 4<\/p>\n<p>Question 7.<br \/>\n&#8211; \u221a49<br \/>\nAnswer:<br \/>\n7<\/p>\n<p>Explanation:<br \/>\nsquare root of 49 = 7 x 7<br \/>\nsquare root of 49 = 7<\/p>\n<p>Question 8.<br \/>\nApproximate \u221a83 to the nearest (a) integer and (b) tenth.<br \/>\nAnswer:<br \/>\n83<\/p>\n<p>Question 9.<br \/>\nWrite \\(1 . \\overline{24}\\) as a mixed number.<\/p>\n<p>Answer:<br \/>\n23<\/p>\n<p>Question 10.<br \/>\nTell whether the triangle is a right triangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-pt-10.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem pt 10\" width=\"224\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\nThe given triangle is not a right triangle.<\/p>\n<p>Explanation:<br \/>\nThe above given triangle is not a right triangle,<br \/>\nright triangle = 90 degrees.<\/p>\n<p>Approximate the distance between the points to the nearest tenth, if necessary.<br \/>\nQuestion 11.<br \/>\n(- 2, 3), (6, 9)<\/p>\n<p>Answer:<br \/>\n(4, 6)<\/p>\n<p>Explanation:<br \/>\n(- 2, 3), (6, 9)<br \/>\n(6-2, 9-3)<br \/>\n(4, 6)<\/p>\n<p>Question 12.<br \/>\n(0, &#8211; 5), (4, 1)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nHow high is the hand of the superhero balloon above the ground?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-pt-13.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem pt 13\" width=\"334\" height=\"682\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-pt-13.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-pt-13-147x300.png 147w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Answer:<br \/>\nThe hand of\u00a0 superhero ballon above the ground = 78 cubic feet.<\/p>\n<p>Explanation:<br \/>\nThe height of the ground = 6 ft<br \/>\nheight from the man hand = 11ft<br \/>\nthe distance from super hero to hand of the man is<br \/>\n6 + 11 + 61<br \/>\n17 + 61<br \/>\n78 cubic feet<\/p>\n<p>Question 14.<br \/>\nThe area of a circular pool cover is 314 square feet. Write and solve an equation to \ufb01nd the diameter of the pool cover. Use 3.14 for \u03c0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-pt-14.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem pt 14\" width=\"201\" height=\"172\" \/><\/p>\n<p>Answer:<br \/>\n46,735.76<\/p>\n<p>Explanation:<br \/>\nArea\u00a0 of the circle = \u03c0 x r x r<br \/>\nArea = 3.14 x 122 x 122<br \/>\nArea = 46,735.76 ft<\/p>\n<p>Question 15.<br \/>\nFive roads form two triangles. What is the value of x? Justify your answer.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Real_Numbers_and_the_Pythagorean_Theorem_Cumulative_Practice\"><\/a>Real Numbers and the Pythagorean Theorem Cumulative Practice<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cp 1\" width=\"299\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-1.png 299w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-1-269x300.png 269w\" sizes=\"(max-width: 299px) 100vw, 299px\" \/><br \/>\nQuestion 1.<br \/>\nThe period T of a pendulum is the time (in seconds) it takes the pendulum to swing back and forth once. The period can be found using the formula T = 1.1 \u221aL, where is the length (in feet) of the pendulum. A pendulum has a length of 4 feet. What is the period of the pendulum?<br \/>\nA. 2.2 sec<br \/>\nB. 3.1 sec<br \/>\nC. 4.4 sec<br \/>\nD. 5.1 sec<\/p>\n<p>Answer:<br \/>\noption C is correct.<\/p>\n<p>Explanation:<br \/>\ngiven that the pendulum has a length of 4 feet.<br \/>\nT = 1.1 l<br \/>\nwhere t = time and l = length<br \/>\nT = 4.4 sec<\/p>\n<p>Question 2.<br \/>\nWhatis the value of y = 5 &#8211; 2x when x = &#8211; 3?<br \/>\nF. &#8211; 1<br \/>\nG. 1<br \/>\nH. 4<br \/>\nI. 11<\/p>\n<p>Answer:<br \/>\noption F is correct.<\/p>\n<p>Explanation:<br \/>\ngiven that x = -3<br \/>\ny = 5 -2 x<br \/>\ny = 5- 2 (-3)<br \/>\ny = 5 -6<br \/>\ny = -1<\/p>\n<p>Question 3.<br \/>\nWhich graph represents the linear equation 3x + 2y = 12?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-3.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cp 3\" width=\"478\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-3.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-3-300x183.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Answer:<br \/>\noption B is correct.<\/p>\n<p>Explanation:<br \/>\nIn the above 4 graphs option B is correct.<br \/>\n3x + 2y = 12<br \/>\nx = 2 and y= 3<br \/>\n3 x 2 + 2 x 3<br \/>\n6 + 6 = 12<\/p>\n<p>Question 4.<br \/>\nWhich expression is equivalent to \\(\\frac{(-3)^{12}}{(-3)^{3}}\\)?<br \/>\nF. (- 3)<sup>4<\/sup><br \/>\nG. (- 3)<sup>9<\/sup><br \/>\nH. 0<sup>9<\/sup><br \/>\nI. 1<sup>9<\/sup><\/p>\n<p>Answer:<br \/>\noption F is correct.<\/p>\n<p>Explanation:<br \/>\ngiven that -3 x -3 x -3 x -3<br \/>\n(-3)\u2074<\/p>\n<p>Question 5.<br \/>\nA football field is 40 yards wide and 120 yards long. Approximate the distance between opposite corners of the football field to the nearest tenth. Show your work and explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-5.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cp 5\" width=\"78\" height=\"61\" \/><\/p>\n<p>Answer:<br \/>\nThe distance between opposite corners of the football field is 80 yards<\/p>\n<p>Explanation:<br \/>\nGiven that the football field is 40 yards and 120 yards long.<br \/>\nthe distance between opposite corners = 120 &#8211; 40<br \/>\n120 &#8211; 40 = 80 yards<\/p>\n<p>Question 6.<br \/>\nA computer consultant charges $50 plus $40 for each hour she works. The consultant charged $650 for one job. This can be represented by the equation below, where h represents the number of hours worked.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-6.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cp 6\" width=\"76\" height=\"55\" \/><br \/>\n40h + 50 = 650<br \/>\nHow many hours did the consultant work?<\/p>\n<p>Answer:<br \/>\nThe consultant work = 7 hours.<\/p>\n<p>Explanation:<br \/>\nGiven that the consultant charges $ 50 + $ 40<br \/>\nfor 1 hour the consultant charges $ 90<br \/>\nThe consultant charged = 650$<br \/>\nseven hours worked = 650<br \/>\n9 x 7 = 63<\/p>\n<p>Question 7.<br \/>\nWhich triangle is not a right triangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-7.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cp 7\" width=\"486\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-7.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-7-300x107.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Answer:<br \/>\noption D is not a right triangle.<\/p>\n<p>Explanation:<br \/>\nGiven that the three triangles are right triangle.<br \/>\nright triangle = 90 degree.<\/p>\n<p>Question 8.<br \/>\nWhat is the distance between (- 3,- 1) and (- 1, &#8211; 5)?<br \/>\nF. \\(\\sqrt{12}\\)<br \/>\nG. \\(\\sqrt{20}\\)<br \/>\nH. \\(\\sqrt{40}\\)<br \/>\nI. \\(\\sqrt{52}\\)<\/p>\n<p>Answer:<br \/>\noption F is correct.<\/p>\n<p>Explanation:<br \/>\ngiven that the distance is (-3, -1) and (-1, -5)<br \/>\n(-3, -1) and (-1, -5)<br \/>\n(-4 , -6)<\/p>\n<p>Question 9.<br \/>\nAn airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). Whatis the total number of miles it flies? Each unit represents 1 mile.<br \/>\nAnswer:<br \/>\nThe total number of miles it flies = 56 miles<\/p>\n<p>Explanation:<br \/>\ngiven that city 1 at (0, 0)<br \/>\ncity 2 at (33, 56)<br \/>\ncity 3 at (23, 32)<br \/>\n33 + 23<br \/>\n56<\/p>\n<p>Question 10.<br \/>\nThe national debt of Country A is $398,038,013,519. The national debt of Country B is $2,137,348,918. Approximately how many times greater is the debt of Country A than the debt of Country B?<br \/>\nA. 2 times greater<br \/>\nB. 20 times greater<br \/>\nC. 133 times greater<br \/>\nD. 200 times greater<\/p>\n<p>Answer:<br \/>\noption B is correct.<\/p>\n<p>Explanation:<br \/>\ncountry A = $398,038,013,519<br \/>\ncountry B = $2,137,348,918.<\/p>\n<p>Question 11.<br \/>\nWhat is the solution of the system?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-11.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cp 11\" width=\"159\" height=\"157\" \/><br \/>\nF.(2, 4)<br \/>\nG. (3, 0)<br \/>\nH.(4, 2)<br \/>\nI. (5, 0)<\/p>\n<p>Answer:<br \/>\noption H is correct.<\/p>\n<p>Explanation:<br \/>\nIn the given graph<br \/>\nthe line x-axis meets on 4 and y-axis meet on 2<br \/>\n(4, 2)<\/p>\n<p>Question 12.<br \/>\nIn the diagram, lines \u2113 and m are parallel. Which angle has the same measure as \u22201?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-12.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cp 12\" width=\"332\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-12.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-12-300x150.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nA. \u22202<br \/>\nB. \u22205<br \/>\nC. \u22207<br \/>\nD. \u22208<\/p>\n<p>Answer:<br \/>\noption D<\/p>\n<p>Explanation:<br \/>\ngiven that l and m are parallel lines.<br \/>\n\u02c2 1 is equal to \u02c28<\/p>\n<p>Question 12.<br \/>\nWhich graph represents the linear equation y = &#8211; 2x &#8211; 2?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-13.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem cp 13\" width=\"468\" height=\"290\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-13.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-9-Real-Numbers-and-the-Pythagorean-Theorem-cp-13-300x186.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Answer:<br \/>\noption F is correct.<\/p>\n<p>Explanation:<br \/>\ngraph F represents the linear equation.<br \/>\ny = -2x -2<\/p>\n<h3>Conclusion<\/h3>\n<p>Hope the information shared regarding the Big Ideas Math Answers Grade 8 Ch 9 Real Numbers and Pythagorean Theorem has shed some light on you. For any further clarifications on the same do leave us your suggestions and we will look into them and respond on the same.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Redefine your true self using the Big Ideas Math Answers Grade 8 Ch 9 Real Numbers and the Pythagorean Theorem. Shed the inhibitions that are holding you back and begin your practice using the BIM Grade 8 Chapter 9 Solutions and clear the exam with better grades. Big Ideas Math Grade 8 Answers Chapter 9 &#8230; <a title=\"Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-9\/\" aria-label=\"More on Big Ideas Math Answers Grade 8 Chapter 9 Real Numbers and the Pythagorean Theorem\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89315,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-9.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31293"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=31293"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31293\/revisions"}],"predecessor-version":[{"id":90337,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31293\/revisions\/90337"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89315"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=31293"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=31293"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=31293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}