{"id":6313,"date":"2022-03-28T21:26:17","date_gmt":"2022-03-28T15:56:17","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6313"},"modified":"2022-04-07T12:54:08","modified_gmt":"2022-04-07T07:24:08","slug":"go-math-grade-8-answer-key-chapter-1-real-numbers","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-1-real-numbers\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 1 Real Numbers"},"content":{"rendered":"<p>The Solutions for Go Math Grade 8 Answer Key Chapter 1 Real Numbers are given in detail here. Get the step by step explanations for all the question in Go Math Grade 8 Chapter 1 Real Numbers Answer Key and start your practice today. You can find the best ways to learn maths by using <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a>. So, Download Go Math Grade 8 Chapter 1 Real Numbers Solution Key and make use of the given resources.<\/p>\n<h2>Go Math Grade 8 Chapter 1 Real Numbers Answer Key<\/h2>\n<p>It is essential for the students to choose the best material to practice the questions. Because by practicing only you can score the highest marks in the exams. Download HMH Go Math Grade 8 Answer Key Chapter 1 Real Numbers PDF for free. Quick learning is possible with our Go Math Grade 8 Chapter 1 Real Numbers Answer Key. Find a better way to make your learning simple by clicking on the below-provided links.<\/p>\n<p><strong>Lesson 1: Rational and Irrational Numbers<\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Rational_and_Irrational_Numbers_-_Page_No._12\">Rational and Irrational Numbers &#8211; Page No. 12<\/a><\/li>\n<li><a href=\"#Rational_and_Irrational_Numbers_-_Page_No._13\">Rational and Irrational Numbers &#8211; Page No. 13<\/a><\/li>\n<li><a href=\"#Rational_and_Irrational_Numbers_-_Page_No._14\">Rational and Irrational Numbers &#8211; Page No. 14<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Lesson 2: Sets of real Numbers<\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Sets_of_real_Numbers_-_Page_No._18\">Sets of real Numbers &#8211; Page No. 18<\/a><\/li>\n<li><a href=\"#Sets_of_real_Numbers_-_Page_No._19\">Sets of real Numbers &#8211; Page No. 19<\/a><\/li>\n<li><a href=\"#Sets_of_real_Numbers_-_Page_No._20\">Sets of real Numbers &#8211; Page No. 20<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Lesson 3: Ordering Real Numbers<\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Ordering_Real_Numbers_-_Page_No._24\">Ordering Real Numbers &#8211; Page No. 24<\/a><\/li>\n<li><a href=\"#Ordering_Real_Numbers_-_Page_No._25\">Ordering Real Numbers &#8211; Page No. 25<\/a><\/li>\n<li><a href=\"#Ordering_Real_Numbers_-_Page_No._26\">Ordering Real Numbers &#8211; Page No. 26<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Model Quiz<\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Model_Quiz_-_Page_No._27\">Model Quiz &#8211; Page No. 27<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Mixed Review<\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Mixed_Review_-_Page_No._28\">Mixed Review &#8211; Page No. 28<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><a id=\"Rational_and_Irrational_Numbers_-_Page_No._12\"><\/a>Guided Practice &#8211; Rational and Irrational Numbers &#8211; Page No. 12<\/h3>\n<p><strong>Write each fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{2}{5}\\) =<\/p>\n<p>Answer:<br \/>\n0.4<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{5}\\) = \\(\\frac{2 \u00d7 2}{5 \u00d7 2}\\) = \\(\\frac{4}{10}\\) = 0.4<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{8}{9}\\) =<\/p>\n<p>Answer:<br \/>\n0.88<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{8}{9}\\) = \\(\\frac{8 \u00d7 10}{9 \u00d7 10}\\) = \\(\\frac{80}{9 \u00d7 10}\\) = \\(\\frac{8.88}{10}\\) = 0.88<\/p>\n<p>Question 3.<br \/>\n3 \\(\\frac{3}{4}\\) =<\/p>\n<p>Answer:<br \/>\n3.75<\/p>\n<p>Explanation:<br \/>\n3 \\(\\frac{3}{4}\\) =\\(\\frac{15}{4}\\) = 3.75<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{7}{10}\\) =<\/p>\n<p>Answer:<br \/>\n0.7<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{7}{10}\\) = 0.7<\/p>\n<p>Question 5.<br \/>\n2 \\(\\frac{3}{8}\\) =<\/p>\n<p>Answer:<br \/>\n2.375<\/p>\n<p>Explanation:<br \/>\n2 \\(\\frac{3}{8}\\) = \\(\\frac{19}{8}\\) = 2.375<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{5}{6}\\) =<\/p>\n<p>Answer:<br \/>\n0.833<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{6}\\) = \\(\\frac{5 \u00d7 10}{6 \u00d7 10}\\) = \\(\\frac{50}{6 \u00d7 10}\\) = \\(\\frac{8.33}{10}\\) = 0.833<\/p>\n<p><strong>Write each decimal as a fraction or mixed number in simplest form<\/strong><\/p>\n<p>Question 7.<br \/>\n0.675<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{27}{40}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{0.675 \u00d7 1000}{1 \u00d7 1000}\\) = \\(\\frac{675}{1000}\\) = \\(\\frac{675\/25}{1000\/25}\\) = \\(\\frac{27}{40}\\)<\/p>\n<p>Question 8.<br \/>\n5.6<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n5 \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5.6 \u00d7 10}{10}\\) = \\(\\frac{56}{10}\\) = 5 \\(\\frac{6}{10}\\) = 5 \\(\\frac{6\/2}{10\/2}\\) = 5 \\(\\frac{3}{5}\\)<\/p>\n<p>Question 9.<br \/>\n0.44<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{11}{25}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{0.44 \u00d7 100}{1 \u00d7 100}\\) = \\(\\frac{44}{100}\\) = \\(\\frac{44\/4}{100\/4}\\) = \\(\\frac{11}{25}\\)<\/p>\n<p>Question 10.<br \/>\n0.\\(\\bar{4}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{9}\\)<\/p>\n<p>Explanation:<br \/>\nLet x = 0.\\(\\bar{4}\\)<br \/>\nNow, 10x = 4.\\(\\bar{4}\\)<br \/>\n10x &#8211; x = 4.\\(\\bar{4}\\) &#8211; 0.\\(\\bar{4}\\)<br \/>\n9x = 4<br \/>\nx = \\(\\frac{4}{9}\\)<\/p>\n<p>Question 11.<br \/>\n0.\\(\\overline { 26 } \\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{26}{99}\\)<\/p>\n<p>Explanation:<br \/>\nLet x = 0.\\(\\overline {26}\\)<br \/>\nNow, 100x = 26.\\(\\overline{26}\\)<br \/>\n100x &#8211; x = 26.\\(\\overline{26}\\) &#8211; 0.\\(\\overline {26}\\)<br \/>\n99x = 26<br \/>\nx = \\(\\frac{26}{99}\\)<\/p>\n<p>Question 12.<br \/>\n0.\\(\\overline { 325 } \\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{325}{999}\\)<\/p>\n<p>Explanation:<br \/>\nLet x = 0.\\(\\overline {325}\\)<br \/>\nNow, 1000x = 325.\\(\\overline{325}\\)<br \/>\n1000x &#8211; x = 325.\\(\\overline{325}\\) &#8211; 0.\\(\\overline {325}\\)<br \/>\n999x = 325<br \/>\nx = \\(\\frac{325}{999}\\)<\/p>\n<p><strong>Solve each equation for x<\/strong><\/p>\n<p>Question 13.<br \/>\nx<sup>2<\/sup> = 144<br \/>\n\u00b1 ______<\/p>\n<p>Answer:<br \/>\n<span id=\"MJXc-Node-14\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">x<\/span><\/span><span id=\"MJXc-Node-15\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-16\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00b1<\/span><\/span><span id=\"MJXc-Node-17\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">12<\/span><\/span><\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> = 144<br \/>\nTaking square roots on both the sides<br \/>\n<span id=\"MathJax-Element-4-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-26\" class=\"mjx-math\"><span id=\"MJXc-Node-27\" class=\"mjx-mrow\"><span id=\"MJXc-Node-28\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-29\" class=\"mjx-mrow\"><span id=\"MJXc-Node-30\" class=\"mjx-msqrt\"><span class=\"mjx-box\"><span class=\"mjx-surd\"><span class=\"mjx-char MJXc-TeX-size1-R\">\u221a<\/span><\/span><span id=\"MJXc-Node-31\" class=\"mjx-mrow\"><span id=\"MJXc-Node-32\" class=\"mjx-mrow\"><span id=\"MJXc-Node-33\" class=\"mjx-msup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-34\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">x<\/span><\/span><\/span><span class=\"mjx-sup\"><span id=\"MJXc-Node-35\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-36\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-37\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00b1<\/span><\/span><span id=\"MJXc-Node-38\" class=\"mjx-msqrt\"><span class=\"mjx-box\"><span class=\"mjx-surd\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221a<\/span><\/span><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">144<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x = <span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-46\" class=\"mjx-math\"><span id=\"MJXc-Node-47\" class=\"mjx-mrow\"><span id=\"MJXc-Node-48\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-49\" class=\"mjx-mrow\"><span id=\"MJXc-Node-53\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00b1<\/span><\/span><span id=\"MJXc-Node-54\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">12<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Question 14.<br \/>\nx<sup>2<\/sup> = \\(\\frac{25}{289}\\)<br \/>\n\u00b1 \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n<span id=\"MJXc-Node-14\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">x <\/span><\/span><span id=\"MJXc-Node-15\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= <\/span><\/span><span id=\"MJXc-Node-16\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00b1<\/span><\/span><span id=\"MJXc-Node-17\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">\\(\\frac{5}{17}\\)<\/span><\/span><\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> = \\(\\frac{25}{289}\\)<br \/>\nTaking square roots on both the sides<br \/>\n<span id=\"MathJax-Element-4-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-26\" class=\"mjx-math\"><span id=\"MJXc-Node-27\" class=\"mjx-mrow\"><span id=\"MJXc-Node-28\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-29\" class=\"mjx-mrow\"><span id=\"MJXc-Node-30\" class=\"mjx-msqrt\"><span class=\"mjx-box\"><span class=\"mjx-surd\"><span class=\"mjx-char MJXc-TeX-size1-R\">\u221a<\/span><\/span><span id=\"MJXc-Node-31\" class=\"mjx-mrow\"><span id=\"MJXc-Node-32\" class=\"mjx-mrow\"><span id=\"MJXc-Node-33\" class=\"mjx-msup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-34\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">x<\/span><\/span><\/span><span class=\"mjx-sup\"><span id=\"MJXc-Node-35\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-36\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-37\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00b1<\/span><\/span><span id=\"MJXc-Node-38\" class=\"mjx-msqrt\"><span class=\"mjx-box\"><span class=\"mjx-surd\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221a\\(\\frac{25}{289}\\)<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x = <span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-46\" class=\"mjx-math\"><span id=\"MJXc-Node-47\" class=\"mjx-mrow\"><span id=\"MJXc-Node-48\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-49\" class=\"mjx-mrow\"><span id=\"MJXc-Node-53\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\"><span id=\"MJXc-Node-16\" class=\"mjx-mo\">\u00b1<\/span><span id=\"MJXc-Node-17\" class=\"mjx-mn\">\\(\\frac{5}{17}\\)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Question 15.<br \/>\nx<sup>3<\/sup> = 216<br \/>\n______<\/p>\n<p>Answer:<br \/>\n<span id=\"MJXc-Node-14\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">x <\/span><\/span><span id=\"MJXc-Node-15\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= <\/span><\/span><span id=\"MJXc-Node-16\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">6<\/span><\/span><\/p>\n<p>Explanation:<br \/>\nx<sup>3<\/sup> = 216<br \/>\nTaking cube roots on both the sides<br \/>\n<span id=\"MathJax-Element-4-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-26\" class=\"mjx-math\"><span id=\"MJXc-Node-27\" class=\"mjx-mrow\"><span id=\"MJXc-Node-28\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-29\" class=\"mjx-mrow\"><span id=\"MJXc-Node-30\" class=\"mjx-msqrt\"><span class=\"mjx-box\"><span class=\"mjx-surd\"><span class=\"mjx-char MJXc-TeX-size1-R\"><span id=\"MJXc-Node-31\" class=\"mjx-mrow\"><span id=\"MJXc-Node-32\" class=\"mjx-mrow\"><span id=\"MJXc-Node-33\" class=\"mjx-msup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-34\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\"><sup>3<\/sup><\/span><\/span><\/span><\/span><\/span><\/span>\u221a<\/span><\/span><span id=\"MJXc-Node-31\" class=\"mjx-mrow\"><span id=\"MJXc-Node-32\" class=\"mjx-mrow\"><span id=\"MJXc-Node-33\" class=\"mjx-msup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-34\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">x<sup>3<\/sup><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-36\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= <span id=\"MJXc-Node-30\" class=\"mjx-msqrt\"><span class=\"mjx-box\"><span id=\"MJXc-Node-31\" class=\"mjx-mrow\"><span id=\"MJXc-Node-32\" class=\"mjx-mrow\"><span id=\"MJXc-Node-33\" class=\"mjx-msup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-34\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\"><sup>3<\/sup><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-38\" class=\"mjx-msqrt\"><span class=\"mjx-box\"><span class=\"mjx-surd\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221a216<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x = 6<\/p>\n<p><strong>Approximate each irrational number to two decimal places without a calculator.<\/strong><\/p>\n<p>Question 16.<br \/>\n\\(\\sqrt { 5 } \\) \u2248 ______<\/p>\n<p>Answer:<br \/>\n2.236<\/p>\n<p>Explanation:<br \/>\nx = \\(\\sqrt { 5 } \\)<br \/>\nThe 5 is in between 4 and 6<br \/>\nTake square root of each year<br \/>\n\u221a4 &lt; \u221a5 &lt; \u221a6<br \/>\n2 &lt; \u221a5 &lt; 3<br \/>\n\u221a5 = 2.2<br \/>\n(2.2)\u00b2 = 4.84<br \/>\n(2.25)\u00b2 = 5.06<br \/>\n(2.5)\u00b3 = 5.29<br \/>\nA good estimate for \u221a5 is 2.25<\/p>\n<p>Question 17.<br \/>\n\\(\\sqrt { 3 } \\) \u2248 ______<\/p>\n<p>Answer:<br \/>\n1.75<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 3 } \\)<br \/>\n1 &lt; 3 &lt; 4<br \/>\n\u221a1 &lt; \u221a3 &lt; \u221a4<br \/>\n1 &lt; \u221a3 &lt; 2<br \/>\n\u221a3 = 1.6<br \/>\n(1.65)\u00b2 = 2.72<br \/>\n(1.7)\u00b2 = 2.89<br \/>\n(1.75)\u00b2 = 3.06<br \/>\nA good estimate for \u221a3 is 1.75<\/p>\n<p>Question 18.<br \/>\n\\(\\sqrt { 10 } \\) \u2248 ______<\/p>\n<p>Answer:<br \/>\n3.15<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 10 } \\)<br \/>\n9 &lt; 10 &lt; 16<br \/>\n\u221a9 &lt; \u221a10 &lt; \u221a16<br \/>\n3 &lt; \u221a10 &lt; 4<br \/>\n\u221a10 = 3.1<br \/>\n(3.1)\u00b2 = 9.61<br \/>\n(3.15)\u00b2 = 9.92<br \/>\n(3.2)\u00b2 = 10.24<br \/>\nA good estimate for \u221a10 is 3.15<\/p>\n<p>Question 19.<br \/>\nWhat is the difference between rational and irrational numbers?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<\/p>\n<p>Rational number can be expressed as a ration of two integers such as 5\/2<br \/>\nIrrational number cannot be expressed as a ratio of two integers such as \u221a13<\/p>\n<p>Explanation:<br \/>\nA rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational.<\/p>\n<h3><a id=\"Rational_and_Irrational_Numbers_-_Page_No._13\"><\/a>1.1 Independent Practice &#8211; Rational and Irrational Numbers &#8211; Page No. 13<\/h3>\n<p>Question 20.<br \/>\nA \\(\\frac{7}{16}\\)-inch-long bolt is used in a machine. What is the length of the bolt written as a decimal?<br \/>\n______ -inch-long<\/p>\n<p>Answer:<br \/>\n0.4375 inch<\/p>\n<p>Explanation:<br \/>\nThe length of the bolt is \\(\\frac{7}{16}\\)-inch<br \/>\nLet, x = \\(\\frac{7}{16}\\)<br \/>\nMultiplying by 125 on both nominator and denominator<br \/>\nx = \\(\\frac{7\u00d7125}{16\u00d7125}\\) = \\(\\frac{875}{2000}\\) =\\(\\frac{437.5}{1000}\\) = 0.4375<\/p>\n<p>Question 21.<br \/>\nThe weight of an object on the moon is \\(\\frac{1}{6}\\) its weight on Earth. Write \\(\\frac{1}{6}\\) as a decimal.<br \/>\n______<\/p>\n<p>Answer:<br \/>\n0.1666<\/p>\n<p>Explanation:<br \/>\nThe weight of the object on the moon is \\(\\frac{1}{6}\\)<br \/>\nLet, x = \\(\\frac{1}{6}\\)<br \/>\nMultiplying by 100 on both nominator and denominator<br \/>\nx = \\(\\frac{1\u00d7100}{6\u00d7100}\\) = \\(\\frac{16.6}{100}\\) =0.166<\/p>\n<p>Question 22.<br \/>\nThe distance to the nearest gas station is 2 \\(\\frac{4}{5}\\) kilometers. What is this distance written as a decimal?<br \/>\n______<\/p>\n<p>Answer:<br \/>\n2.8<\/p>\n<p>Explanation:<br \/>\nThe distance of the nearest gas station is 2 \\(\\frac{4}{5}\\)<br \/>\nLet, x = 2 \\(\\frac{4}{5}\\)<br \/>\nMultiplying by 100 on both nominator and denominator<br \/>\nx = 2 \\(\\frac{4\u00d7100}{5\u00d7100}\\) = \\(\\frac{80}{100}\\) =0.8<\/p>\n<p>Question 23.<br \/>\nA baseball pitcher has pitched 98 \\(\\frac{2}{3}\\) innings. What is the number of innings written as a decimal?<br \/>\n______<\/p>\n<p>Answer:<br \/>\n98.6<\/p>\n<p>Explanation:<br \/>\nA baseball pitcher has pitched 98 \\(\\frac{2}{3}\\) innings.<br \/>\n98 \\(\\frac{2}{3}\\) = 98 + 2\/3<br \/>\n= (294\/3) + (2\/3)<br \/>\n296\/3<br \/>\n98.6<\/p>\n<p>Question 24.<br \/>\nA heartbeat takes 0.8 second. How many seconds is this written as a fraction?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nA heartbeat takes 0.8 seconds.<br \/>\n0.8<br \/>\nThere are 8 tenths.<br \/>\n8\/10 = 4\/5<\/p>\n<p>Question 25.<br \/>\nThere are 26.2 miles in a marathon. Write the number of miles using a fraction.<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n26\\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThere are 26.2 miles in a marathon.<br \/>\n26.2 miles<br \/>\n262\/10<br \/>\n131\/5<br \/>\n26 1\/5 miles<\/p>\n<p>Question 26.<br \/>\nThe average score on a biology test was 72.\\(\\bar{1}\\). Write the average score using a fraction.<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n80 \\(\\frac{1}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe average score on a biology test was 72.\\(\\bar{1}\\).<br \/>\n72.\\(\\bar{1}\\)<br \/>\nLet x = 72.\\(\\bar{1}\\)<br \/>\n10x = 10(72.\\(\\bar{1}\\))<br \/>\n10x = 721.1<br \/>\n-x = -0.1<br \/>\n9x = 721<br \/>\nx = 721\/9<br \/>\nx = 80 1\/9<\/p>\n<p>Question 27.<br \/>\nThe metal in a penny is worth about 0.505 cent. How many cents is this written as a fraction?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{101}{200}\\)<\/p>\n<p>Explanation:<br \/>\nThe metal in a penny is worth about 0.505 cent.<br \/>\n0.505 cent<br \/>\n505 thousandths<br \/>\n505\/1000<br \/>\n101\/200 cents<\/p>\n<p>Question 28.<br \/>\nMultistep An artist wants to frame a square painting with an area of 400 square inches. She wants to know the length of the wood trim that is needed to go around the painting.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 1: Rational and Irrational Numbers img 1\" width=\"389\" height=\"404\" \/><br \/>\na. If x is the length of one side of the painting, what equation can you set up to find the length of a side?<br \/>\nx<sup>2<\/sup> = ______<\/p>\n<p>Answer:<br \/>\nx\u00b2 = 400<\/p>\n<p>Explanation:<br \/>\nThe area of a square is the square of its equal side, x<br \/>\nx\u00b2 = 400<\/p>\n<p>Question 28.<br \/>\nb. Solve the equation you wrote in part a. How many solutions does the equation have?<br \/>\nx = \u00b1 ______<\/p>\n<p>Answer:<br \/>\nx = \u00b1 20<\/p>\n<p>Explanation:<br \/>\nTake the square root on both sides. Solve<br \/>\nx = \u00b1 20<\/p>\n<p>Question 28.<br \/>\nc. Do all of the solutions that you found in part b make sense in the context of the problem? Explain.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nNo. Both values of x do not make sense.<\/p>\n<p>Explanation:<br \/>\nThe length cannot be negative, hence negative value does not make sense.<br \/>\nNo. Both values of x do not make sense.<\/p>\n<p>Question 28.<br \/>\nd. What is the length of the wood trim needed to go around the painting?<br \/>\nP = ______ inches<\/p>\n<p>Answer:<br \/>\nLength P = 20 + 2y<\/p>\n<h3><a id=\"Rational_and_Irrational_Numbers_-_Page_No._14\"><\/a>Rational and Irrational Numbers &#8211; Page No. 14<\/h3>\n<p>Question 29.<br \/>\nAnalyze Relationships To find \\(\\sqrt { 15 } \\), Beau found 3<sup>2<\/sup> = 9 and 4<sup>2<\/sup> = 16. He said that since 15 is between 9 and 16, \\(\\sqrt { 15 } \\) must be between 3 and 4. He thinks a good estimate for \\(\\sqrt { 15 } \\) is \\(\\frac { 3+4 }{ 2 } \\) = 3.5. Is Beau\u2019s estimate high, low, or correct? Explain.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n3.85<\/p>\n<p>Explanation:<br \/>\n15 is closer to 16<br \/>\n\u221a15 is closer to \u221a16<br \/>\nBeau&#8217;s estimate is low.<br \/>\n(3.8)\u00b2 = 14.44<br \/>\n(3.85)\u00b2 = 14.82<br \/>\n(3.9)\u00b2 = 15.21<br \/>\n\u221a15 is 3.85<\/p>\n<p>Question 30.<br \/>\nJustify Reasoning What is a good estimate for the solution to the equation x<sup>3<\/sup> = 95? How did you come up with your estimate?<br \/>\nx \u2248 ______<\/p>\n<p>Answer:<br \/>\nx \u2248\u00a0 4.55<\/p>\n<p>Explanation:<br \/>\n<sup>3<\/sup>\u221ax = 95<br \/>\nx = <sup>3<\/sup>\u221a95<br \/>\n64 &lt; 95 &lt; 125<br \/>\nTake the cube root of each number<br \/>\n<sup>3<\/sup>\u221a64 &lt; <sup>3<\/sup>\u221a95\u00a0 &lt; <sup>3<\/sup>\u221a125<br \/>\n4 &lt; <sup>3<\/sup>\u221a95 &lt; 5<br \/>\n<sup>3<\/sup>\u221a95 = 4.6<br \/>\n(4.5)\u00b3 = 91.125<br \/>\n(4.55)\u00b3 = 94.20<br \/>\n(4.6)\u00b3 = 97.336<br \/>\n<sup>3<\/sup>\u221a95 = 4.55<\/p>\n<p>Question 31.<br \/>\nThe volume of a sphere is 36\u03c0 ft<sup>3<\/sup>. What is the radius of the sphere? Use the formula V = \\(\\frac { 4 }{ 3 } \\)\u03c0r<sup>3<\/sup> to find your answer.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 1: Rational and Irrational Numbers img 2\" width=\"485\" height=\"585\" \/><br \/>\nr = ______<\/p>\n<p>Answer:<br \/>\nr = 3<\/p>\n<p>Explanation:<br \/>\nV = 4\/3 \u03c0r\u00b3<br \/>\n36\u03c0 = 4\/3 \u03c0r\u00b3<br \/>\nr\u00b3 = 36\u03c0\/\u03c0 . 3\/4<br \/>\nr\u00b3 = 27<br \/>\nr = <sup>3<\/sup>\u221a27<br \/>\nr = 3<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 32.<br \/>\nDraw Conclusions Can you find the cube root of a negative number? If so, is it positive or negative? Explain your reasoning.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nYes<\/p>\n<p>Explanation:<br \/>\nYes. The cube root of a negative number would be negative. Because the product of three negative signs is always negative.<\/p>\n<p>Question 33.<br \/>\nMake a Conjecture Evaluate and compare the following expressions.<br \/>\n\\(\\sqrt { \\frac { 4 }{ 25 } } \\) and \\(\\frac { \\sqrt { 4 } }{ \\sqrt { 25 } } \\) \\(\\sqrt { \\frac { 16 }{ 81 } } \\) and \\(\\frac { \\sqrt { 16 } }{ \\sqrt { 81 } } \\) \\(\\sqrt { \\frac { 36 }{ 49 } } \\) and\\(\\frac { \\sqrt { 36 } }{ \\sqrt { 49 } } \\)<br \/>\nUse your results to make a conjecture about a division rule for square roots. Since division is multiplication by the reciprocal, make a conjecture about a multiplication rule for square roots.<br \/>\nExpressions are: _____________<\/p>\n<p>Answer:<br \/>\nEvaluating and comparing<br \/>\n\u221a4\/25 = 2\/5<br \/>\n\u221a16\/81 = 4\/9<br \/>\n\u221a36\/49 = 6\/7<br \/>\nConjecture about a division rule for square roots<br \/>\n\u221aa\/\u221ab = \u221a(a\/b)<br \/>\nConjecture about a multiplication rule for square roots<br \/>\n\u221aa \u00d7 \u221ab<\/p>\n<p>Question 34.<br \/>\nPersevere in Problem Solving<br \/>\nThe difference between the solutions to the equation x<sup>2<\/sup> = a is 30. What is a? Show that your answer is correct.<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n30<\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> = a<br \/>\nx = \u00b1\u221aa<br \/>\n\u221aa &#8211; (-\u221aa) = 30<br \/>\n\u221aa + \u221aa = 30<br \/>\n2\u221aa = 30<br \/>\n\u221aa = 15<br \/>\na = 225<br \/>\nx<sup>2<\/sup> = 225<br \/>\nx = \u00b1225<br \/>\nx = \u00b115<br \/>\n15 &#8211; (-15) = 15 + 15 = 30<\/p>\n<h3><a id=\"Sets_of_real_Numbers_-_Page_No._18\"><\/a>Guided Practice &#8211; Sets of real Numbers &#8211; Page No. 18<\/h3>\n<p><strong>Write all names that apply to each number.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{7}{8}\\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt { 36 } \\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 36 } \\) = 6<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt { 24 } \\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Question 4.<br \/>\n0.75<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<\/p>\n<p>Question 5.<br \/>\n0<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<\/p>\n<p>Question 6.<br \/>\n\u2212\\(\\sqrt { 100 } \\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<\/p>\n<p>Explanation:<br \/>\n\u2212\\(\\sqrt { 100 } \\) = &#8211; 10<\/p>\n<p>Question 7.<br \/>\n5.\\(\\overline { 45 } \\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<\/p>\n<p>Question 8.<br \/>\n\u2212\\(\\frac{18}{6}\\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<\/p>\n<p>Explanation:<br \/>\n\u2212\\(\\frac{18}{6}\\) = -3<\/p>\n<p><strong>Tell whether the given statement is true or false. Explain your choice.<\/strong><\/p>\n<p>Question 9.<br \/>\nAll whole numbers are rational numbers.<br \/>\ni. True<br \/>\nii. False<\/p>\n<p>Answer:<br \/>\ni. True<\/p>\n<p>Explanation:<br \/>\nAll whole numbers are rational numbers.<br \/>\nWhole numbers are a subset of the set of rational numbers and can be written as ratio of the whole number to 1.<\/p>\n<p>Question 10.<br \/>\nNo irrational numbers are whole numbers.<br \/>\ni. True<br \/>\nii. False<\/p>\n<p>Answer:<br \/>\ni. True<\/p>\n<p>Explanation:<br \/>\nTrue. Whole numbers are ration numbers.<\/p>\n<p><strong>Identify the set of numbers that best describes each situation. Explain your choice.<\/strong><\/p>\n<p>Question 11.<br \/>\nthe change in the value of an account when given to the nearest dollar<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\nc. Integer Numbers<\/p>\n<p>Explanation:<br \/>\nThe change can be a whole dollar amount and can be positive, negative or zero.<\/p>\n<p>Question 12.<br \/>\nthe markings on a standard ruler<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 2: Sets of real Numbers img 3\" width=\"234\" height=\"576\" \/><br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\nb. Rational Numbers<\/p>\n<p>Explanation:<br \/>\nThe ruler is marked every 1\/16t inch.<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 13.<br \/>\nWhat are some ways to describe the relationships between sets of numbers?<\/p>\n<p>Answer:<br \/>\nThere are two ways that we have been using until now to describe the relationships between sets of numbers<\/p>\n<ul>\n<li>Using a scheme or a diagram as the one on page 15.<\/li>\n<li>Verbal description, for example, &#8220;All irrational numbers are real numbers.&#8221;<\/li>\n<\/ul>\n<h3><a id=\"Sets_of_real_Numbers_-_Page_No._19\"><\/a>1.2 Independent Practice &#8211; Sets of real Numbers &#8211; Page No. 19<\/h3>\n<p><strong>Write all names that apply to each number. Then place the numbers in the correct location on the Venn diagram.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 2: Sets of real Numbers img 4\" width=\"571\" height=\"329\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt { 9 } \\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 9 } \\) = 3<\/p>\n<p>Question 15.<br \/>\n257<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<\/p>\n<p>Question 16.<br \/>\n\\(\\sqrt { 50 } \\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Question 17.<br \/>\n8 \\(\\frac{1}{2}\\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<\/p>\n<p>Question 18.<br \/>\n16.6<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<\/p>\n<p>Question 19.<br \/>\n\\(\\sqrt { 16 } \\)<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 16 } \\) = 4<\/p>\n<p><strong>Identify the set of numbers that best describes each situation. Explain your choice.<\/strong><\/p>\n<p>Question 20.<br \/>\nthe height of an airplane as it descends to an airport runway<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\nd. Whole Numbers<\/p>\n<p>Explanation:<br \/>\nWhole. The height of an airplane as it descents to an airport runway is a whole number greater than 0<\/p>\n<p>Question 21.<br \/>\nthe score with respect to par of several golfers: 2, \u2013 3, 5, 0, \u2013 1<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integer Numbers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\nc. Integer Numbers<\/p>\n<p>Explanation:<br \/>\nIntegers. The scores are counting numbers, their opposites, and zero.<\/p>\n<p>Question 22.<br \/>\nCritique Reasoning Ronald states that the number \\(\\frac{1}{11}\\) is not rational because, when converted into a decimal, it does not terminate. Nathaniel says it is rational because it is a fraction. Which boy is correct? Explain.<br \/>\ni. Ronald<br \/>\nii. Nathaniel<\/p>\n<p>Answer:<br \/>\nii. Nathaniel<\/p>\n<p>Explanation:<br \/>\nNathaniel is correct.<br \/>\nA fraction is a rational real number, even if it is not a terminating decimal.<\/p>\n<h3><a id=\"Sets_of_real_Numbers_-_Page_No._20\"><\/a>Sets of real Numbers &#8211; Page No. 20<\/h3>\n<p>Question 23.<br \/>\nCritique Reasoning The circumference of a circular region is shown. What type of number best describes the diameter of the circle? Explain your answer.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 2: Sets of real Numbers img 5\" width=\"134\" height=\"120\" \/><br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Irrational Numbers<br \/>\nd. Integers<br \/>\ne. Whole Numbers<\/p>\n<p>Answer:<br \/>\ne. Whole Numbers<\/p>\n<p>Explanation:<br \/>\nCircumference of the circle<br \/>\nA = 2\u03c0r<br \/>\n\u03c0 = 2\u03c0r<br \/>\nDiameter is twice the radius<br \/>\n2r = 1<br \/>\nWhole<\/p>\n<p>Question 24.<br \/>\nCritical Thinking A number is not an integer. What type of number can it be?<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\nb. Rational Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Question 25.<br \/>\nA grocery store has a shelf with half-gallon containers of milk. What type of number best represents the total number of gallons?<br \/>\nOptions:<br \/>\na. Real Numbers<br \/>\nb. Rational Numbers<br \/>\nc. Integers<br \/>\nd. Whole Numbers<br \/>\ne. Irrational Numbers<\/p>\n<p>Answer:<br \/>\nb. Rational Numbers<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 26.<br \/>\nExplain the Error Katie said, \u201cNegative numbers are integers.\u201d What was her error?<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nHer error is that she stated that all negative numbers are integers. Some negative numbers are integers such as -4 but some are not such an -0.8<\/p>\n<p>Question 27.<br \/>\nJustify Reasoning Can you ever use a calculator to determine if a number is rational or irrational? Explain.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nNot always.<\/p>\n<p>Explanation:<br \/>\nNot always.<br \/>\nIf the calculator shows a terminating decimal, the number is rational but otherwise, it is not possible as you can only see a few digits.<\/p>\n<p>Question 28.<br \/>\nDraw Conclusions The decimal 0.\\(\\bar{3}\\) represents \\(\\frac{1}{3}\\). What type of number best describes 0.\\(\\bar{9}\\) , which is 3 \u00d7 0.\\(\\bar{3}\\)? Explain.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n1<\/p>\n<p>Explanation:<br \/>\nlet x = 0.9999999<br \/>\n10x = 9.99999999<br \/>\n10x = 9 + 0.999999999<br \/>\n10x = 9 + x<br \/>\n9x = 9<br \/>\nx=1.<\/p>\n<p>Question 29.<br \/>\nCommunicate Mathematical Ideas Irrational numbers can never be precisely represented in decimal form. Why is this?<\/p>\n<p>Answer:<br \/>\nBecause irrational numbers are nonrepeating, otherwise they could be represented as a fraction. Although a potential counter-example to this claim is that some irrational numbers can only be represented in decimal form, for example, 0.1234567891011121314151617\u2026, 0.24681012141618202224\u2026, 0.101101110111101111101111110\u2026 are all irrational numbers.<\/p>\n<h3><a id=\"Ordering_Real_Numbers_-_Page_No._24\"><\/a>Guided Practice &#8211; Ordering Real Numbers &#8211; Page No. 24<\/h3>\n<p><strong>Compare. Write &lt;, &gt;, or =.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\sqrt { 3 } \\) + 2 ________ \\(\\sqrt { 3 } \\) + 3<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 3 } \\) + 2 &lt; \\(\\sqrt { 3 } \\) + 3<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 3 } \\) is between 1 and 2<br \/>\n\\(\\sqrt { 3 } \\) + 2 is between 3 and 4<br \/>\n\\(\\sqrt { 3 } \\) + 3 is between 4 and 5<br \/>\n\\(\\sqrt { 3 } \\) + 2 &lt; \\(\\sqrt { 3 } \\) + 3<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt { 11 } \\) + 15 _______ \\(\\sqrt { 8 } \\) + 15<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 11 } \\) + 15 &gt; \\(\\sqrt { 8 } \\) + 15<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 11 } \\) is between 3 and 4<br \/>\n\\(\\sqrt { 8 } \\) is between 2 and 3<br \/>\n\\(\\sqrt { 11 } \\) + 15 is between 18 and 19<br \/>\n\\(\\sqrt { 8 } \\) + 15 is between 17 and 18<br \/>\n\\(\\sqrt { 11 } \\) + 15 &gt; \\(\\sqrt { 8 } \\) + 15<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt { 6 } \\) + 5 _______ 6 + \\(\\sqrt { 5 } \\)<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 6 } \\) + 5 &lt; 6 + \\(\\sqrt { 5 } \\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 6 } \\) is between 2 and 3<br \/>\n\\(\\sqrt { 5 } \\) is between 2 and 3<br \/>\n\\(\\sqrt { 6 } \\) is between 7 and 8<br \/>\n\\(\\sqrt { 5 } \\) is between 8 and 9<br \/>\n\\(\\sqrt { 6 } \\) + 5 &lt; 6 + \\(\\sqrt { 5 } \\)<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt { 9 } \\) + 3 _______ 9 + \\(\\sqrt { 3 } \\)<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 9 } \\) + 3 &lt; 9 + \\(\\sqrt { 3 } \\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 9 } \\) + 3<br \/>\n9 + \\(\\sqrt { 3 } \\)<br \/>\n\\(\\sqrt { 3 } \\) is between 1 and 2<br \/>\n\\(\\sqrt { 9 } \\) + 3 = 3 + 3 = 6<br \/>\n9 + \\(\\sqrt { 3 } \\) is between 10 and 11<br \/>\n\\(\\sqrt { 9 } \\) + 3 &lt; 9 + \\(\\sqrt { 3 } \\)<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt { 17 } \\) &#8211; 3 _______ -2 + \\(\\sqrt { 5 } \\)<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 17 } \\) &#8211; 3 &gt; -2 + \\(\\sqrt { 5 } \\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 17 } \\) is between 4 and 5<br \/>\n\\(\\sqrt { 5 } \\) is between 2 and 3<br \/>\n\\(\\sqrt { 17 } \\) &#8211; 3 is between 1 and 2<br \/>\n-2 + \\(\\sqrt { 5 } \\) is between 0 and 1<br \/>\n\\(\\sqrt { 17 } \\) &#8211; 3 &gt; -2 + \\(\\sqrt { 5 } \\)<\/p>\n<p>Question 6.<br \/>\n10 &#8211; \\(\\sqrt { 8 } \\) _______ 12 &#8211; \\(\\sqrt { 2 } \\)<\/p>\n<p>Answer:<br \/>\n10 &#8211; \\(\\sqrt { 8 } \\) &lt; 12 &#8211; \\(\\sqrt { 2 } \\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 8 } \\) is between 2 and 3<br \/>\n\\(\\sqrt { 2 } \\) is between 1 and 2<br \/>\n10 &#8211; \\(\\sqrt { 8 } \\) is between 8 and 7<br \/>\n12 &#8211; \\(\\sqrt { 2 } \\) is between 11 and 10<br \/>\n10 &#8211; \\(\\sqrt { 8 } \\) &lt; 12 &#8211; \\(\\sqrt { 2 } \\)<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt { 7 } \\) + 2 _______ \\(\\sqrt { 10 } \\) &#8211; 1<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 7 } \\) + 2 &gt; \\(\\sqrt { 10 } \\) &#8211; 1<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 7 } \\) is between 2 and 3<br \/>\n\\(\\sqrt { 10 } \\) is between 3 and 4<br \/>\n\\(\\sqrt { 7 } \\) + 2 is between 4 and 5<br \/>\n\\(\\sqrt { 10 } \\) &#8211; 1 is between 2 and 3<br \/>\n\\(\\sqrt { 7 } \\) + 2 &gt; \\(\\sqrt { 10 } \\) &#8211; 1<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt { 17 } \\) + 3 _______ 3 + \\(\\sqrt { 11 } \\)<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 17 } \\) + 3 &gt; 3 + \\(\\sqrt { 11 } \\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 17 } \\) is between 4 and 5<br \/>\n\\(\\sqrt { 11 } \\) is between 3 and 4<br \/>\n\\(\\sqrt { 17 } \\) + 3 is between 7 and 8<br \/>\n3 + \\(\\sqrt { 11 } \\) is between 6 and 7<br \/>\n\\(\\sqrt { 17 } \\) + 3 &gt; 3 + \\(\\sqrt { 11 } \\)<\/p>\n<p>Question 9.<br \/>\nOrder \\(\\sqrt { 3 } \\), 2 \u03c0, and 1.5 from least to greatest. Then graph them on the number line.<br \/>\n\\(\\sqrt { 3 } \\) is between _________ and _____________ , so \\(\\sqrt { 3 } \\) \u2248 ____________.<br \/>\n\u03c0 \u2248 3.14, so 2 \u03c0 \u2248 _______________.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 3: Ordering Real Numbers img 6\" width=\"510\" height=\"63\" \/><br \/>\nFrom least to greatest, the numbers are ______________, _____________________ ,_________________.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n1.5, \\(\\sqrt { 3 } \\), 2 \u03c0<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 3 } \\) is between 1.7 and 1.75<br \/>\n\u03c0 = 3.14; 2 \u03c0 = 6.28<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-1-300x46.png\" alt=\"grade 8 chapter 1 image 1\" width=\"300\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-1-300x46.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-1-768x117.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-1.png 932w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n1.5, \\(\\sqrt { 3 } \\), 2 \u03c0<\/p>\n<p>Question 10.<br \/>\nFour people have found the perimeter of a forest using different methods. Their results are given in the table. Order their calculations from greatest to least.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 3: Ordering Real Numbers img 7\" width=\"353\" height=\"198\" \/><br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 17 } \\) &#8211; 2, 1+ \u03c0\/2, 2.5, 12\/5<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 17 } \\) &#8211; 2<br \/>\n\\(\\sqrt { 17 } \\) is between 4 and 5<br \/>\nSince, 17 is closer to 16, the estimated value is 4.1<br \/>\n1+ \u03c0\/2<br \/>\n1 + (3.14\/2) = 2.57<br \/>\n12\/5 = 2.4<br \/>\n2.5<br \/>\n\\(\\sqrt { 17 } \\) &#8211; 2, 1+ \u03c0\/2, 2.5, 12\/5<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 11.<br \/>\nExplain how to order a set of real numbers.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nEvaluate the given numbers and write in decimal form. Plot on number line and arrange the numbers accordingly.<\/p>\n<h3><a id=\"Ordering_Real_Numbers_-_Page_No._25\"><\/a>Independent Practice &#8211; Ordering Real Numbers &#8211; Page No. 25<\/h3>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt { 7 } \\), 2, \\(\\frac { \\sqrt { 8 } }{ 2 } \\)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n\\(\\frac { \\sqrt { 8 } }{ 2 } \\), 2, \\(\\sqrt { 7 } \\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 7 } \\), 2, \\(\\frac { \\sqrt { 8 } }{ 2 } \\)<br \/>\n\\(\\sqrt { 7 } \\) is between 2 and 3<br \/>\nSince 7 is closer to 9, (2.65)\u00b2 = 7.02, hence the estimated value is 2.65<br \/>\n\\(\\frac { \\sqrt { 8 } }{ 2 } \\)<br \/>\n\\(\\sqrt { 8 } \\) is between 2 and 3<br \/>\nSince 8 is closer to 9, (2.85)\u00b2 = 8.12, hence the estimated value is 2.85<br \/>\n2.85\/2 = 1.43<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-3-300x48.png\" alt=\"grade 8 chapter 1 image 3\" width=\"300\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-3-300x48.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-3-768x123.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-3.png 945w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\\(\\frac { \\sqrt { 8 } }{ 2 } \\), 2, \\(\\sqrt { 7 } \\)<\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt { 10 } \\), \u03c0, 3.5<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n\u03c0, \\(\\sqrt { 10 } \\), 3.5<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 10 } \\), \u03c0, 3.5<br \/>\n\\(\\sqrt { 10 } \\) is between 3 and 4<br \/>\nSince, 10 is closer to 9, (3.15)\u00b2 = 9.92, hence the estimated value is 3.15<br \/>\n\u03c0 = 3.14<br \/>\n3.5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-4-300x45.png\" alt=\"grade 8 chapter 1 image 4\" width=\"300\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-4-300x45.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-4-768x116.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-4.png 952w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u03c0, \\(\\sqrt { 10 } \\), 3.5<\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt { 220 } \\), \u221210, \\(\\sqrt { 100 } \\), 11.5<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n-10, \u221a100, 11.5, \u221a220<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 220 } \\), \u221210, \\(\\sqrt { 100 } \\), 11.5<br \/>\n196 &lt; 220 &lt; 225<br \/>\n\u221a196 &lt; \u221a220 &lt; \u221a225<br \/>\n14 &lt; \u221a220 &lt; 15<br \/>\n\u221a220 = 14.5<br \/>\n\u221a100 = 10<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-5-300x30.png\" alt=\"grade 8 chapter 1 image 5\" width=\"300\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-5-300x30.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-5-768x76.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-5.png 932w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n-10, \u221a100, 11.5, \u221a220<\/p>\n<p>Question 15.<br \/>\n\\(\\sqrt { 8 } \\), \u22123.75, 3, \\(\\frac{9}{4}\\)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n\u22123.75, \\(\\frac{9}{4}\\), \\(\\sqrt { 8 } \\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 8 } \\), \u22123.75, 3, \\(\\frac{9}{4}\\)<br \/>\n\\(\\sqrt { 8 } \\) is between 2 and 3<br \/>\nSince, 8 is closer to 9, (2.85)\u00b2 = 8.12, hence the estimated value is 2.85<br \/>\n-3.75 = 3<br \/>\n9\/4 = 2.25<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-6-2-300x46.png\" alt=\"grade 8 chapter 1 image 6\" width=\"300\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-6-2-300x46.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-6-2-768x117.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-6-2.png 955w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u22123.75, \\(\\frac{9}{4}\\), \\(\\sqrt { 8 } \\)<\/p>\n<p>Question 16.<br \/>\nYour sister is considering two different shapes for her garden. One is a square with side lengths of 3.5 meters, and the other is a circle with a diameter of 4 meters.<br \/>\na. Find the area of the square.<br \/>\n_______ m<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n(3.5)\u00b2 = 12.25<\/p>\n<p>Explanation:<br \/>\nArea of the square = x\u00b2<br \/>\nArea = (3.5)\u00b2 = 12.25<\/p>\n<p>Question 16.<br \/>\nb. Find the area of the circle.<br \/>\n_______ m<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n\u03c0(2)\u00b2 = 12.56<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0r\u00b2 where r = d\/2 = 4\/2 = 2<br \/>\nArea = \u03c0(2)\u00b2 = 12.56<\/p>\n<p>Question 16.<br \/>\nc. Compare your answers from parts a and b. Which garden would give your sister the most space to plant?<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n12.25 &lt; 12.56<br \/>\nThe circle will give more space<\/p>\n<p>Question 17.<br \/>\nWinnie measured the length of her father\u2019s ranch four times and got four different distances. Her measurements are shown in the table.<br \/>\na. To estimate the actual length, Winnie first approximated each distance to the nearest hundredth. Then she averaged the four numbers. Using a calculator, find Winnie\u2019s estimate.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 3: Ordering Real Numbers img 8\" width=\"360\" height=\"123\" \/><br \/>\n______<\/p>\n<p>Answer:<br \/>\n7.4815<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 60 } \\) = 7.75<br \/>\n58\/8 = 7.25<br \/>\n7.3333<br \/>\n7 3\/5 = 7.60<br \/>\nAverage = (7.75 + 7.25 + 7.33 + 7.60)\/4 = 7.4815<\/p>\n<p>Question 17.<br \/>\nb. Winnie\u2019s father estimated the distance across his ranch to be \\(\\sqrt { 56 } \\) km. How does this distance compare to Winnie\u2019s estimate?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThey are nearly identical<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 56 } \\) = 7.4833<br \/>\nThey are nearly identical<\/p>\n<p><strong>Give an example of each type of number.<\/strong><\/p>\n<p>Question 18.<br \/>\na real number between \\(\\sqrt { 13 } \\) and \\(\\sqrt { 14 } \\)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA real number between \\(\\sqrt { 13 } \\) and \\(\\sqrt { 14 } \\)<br \/>\nExample: 3.7<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 13 } \\) = 3.61<br \/>\n\\(\\sqrt { 13 } \\) = 3.74<br \/>\nA real number between \\(\\sqrt { 13 } \\) and \\(\\sqrt { 14 } \\)<br \/>\nExample: 3.7<\/p>\n<p>Question 19.<br \/>\nan irrational number between 5 and 7<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAn irrational number between 5 and 7<br \/>\nExample: \\(\\sqrt { 29 } \\)<\/p>\n<p>Explanation:<br \/>\n5\u00b2 = 25 and 7\u00b2 = 49<br \/>\nAn irrational number between 5 and 7<br \/>\nExample: \\(\\sqrt { 29 } \\)<\/p>\n<h3><a id=\"Ordering_Real_Numbers_-_Page_No._26\"><\/a>Ordering Real Numbers &#8211; Page No. 26<\/h3>\n<p>Question 20.<br \/>\nA teacher asks his students to write the numbers shown in order from least to greatest. Paul thinks the numbers are already in order. Sandra thinks the order should be reversed. Who is right?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 3: Ordering Real Numbers img 9\" width=\"271\" height=\"188\" \/><br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nNeither are correct<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 115 } \\), 115\/11, 10.5624<br \/>\n\\(\\sqrt { 115 } \\) is between 10 and 11<br \/>\nSince, 115 is closer to 121, (10.7)\u00b2 = 114.5, hence the estimated value is 10.7<br \/>\n115\/11 = 10.4545<br \/>\n10.5624<br \/>\nNeither are correct<\/p>\n<p>Question 21.<br \/>\nMath History<br \/>\nThere is a famous irrational number called Euler\u2019s number, symbolized with an e. Like \u03c0, its decimal form never ends or repeats. The first few digits of e are 2.7182818284.<br \/>\na. Between which two square roots of integers could you find this number?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe square of e lies between 7 and 8<br \/>\n2.718281828<br \/>\n(2.72)\u00b2 = 7.3984<br \/>\nHence, it lies between \\(\\sqrt { 7 } \\) = 2.65 and \\(\\sqrt { 8 } \\) = 2.82<\/p>\n<p>Question 21.<br \/>\nb. Between which two square roots of integers can you find \u03c0?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n3.142<br \/>\n(3.14)\u00b2 = 9.8596<br \/>\nHence. it lies between \\(\\sqrt { 9 } \\) = 3 and \\(\\sqrt { 10 } \\) = 3.16<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 22.<br \/>\nAnalyze Relationships<br \/>\nThere are several approximations used for \u03c0, including 3.14 and \\(\\frac{22}{7}\\). \u03c0 is approximately 3.14159265358979 . . .<br \/>\na. Label \u03c0 and the two approximations on the number line.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Lesson 3: Ordering Real Numbers img 10\" width=\"285\" height=\"45\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-7-300x39.png\" alt=\"grade 8 chapter 1 image 7\" width=\"300\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-7-300x39.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-7.png 697w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 22.<br \/>\nb. Which of the two approximations is a better estimate for \u03c0? Explain.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nAs we can see from the number line, 22\/7 is closer to \u03c0, so we can conclude that 22\/7 is a better estimation for \u03c0.<\/p>\n<p>Question 22.<br \/>\nc. Find a whole number x so that the ratio \\(\\frac{x}{113}\\) is a better estimate for \u03c0 than the two given approximations.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n355\/113 is a better estimation for \u03c0, because 355\/113 = 3.14159292035 = 3.14159265358979 = \u03c0<\/p>\n<p>Question 23.<br \/>\nCommunicate Mathematical Ideas<br \/>\nWhat is the fewest number of distinct points that must be graphed on a number line, in order to represent natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers? Explain.<br \/>\n_______ points<\/p>\n<p>Answer:<br \/>\n2 points<\/p>\n<p>Explanation:<br \/>\nThere need to be plotting of at least 2 points because a rational number can never be equal to an irrational number. So let&#8217;s say 5 points are the same among six but the 6th will be different as there both rational numbers and irrational numbers included.<\/p>\n<p>Question 24.<br \/>\nCritique Reasoning<br \/>\nJill says that 12.\\(\\bar{6}\\) is less than 12.63. Explain her error.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n12.\\(\\bar{6}\\) = 12.666<br \/>\n12.\\(\\bar{6}\\) &gt; 12.63<\/p>\n<h3><a id=\"Model_Quiz_-_Page_No._27\"><\/a>1.1 Rational and Irrational Numbers &#8211; Model Quiz &#8211; Page No. 27<\/h3>\n<p><strong>Write each fraction as a decimal or each decimal as a fraction.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{7}{20}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n0.35<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{7}{20}\\) = 0.35<\/p>\n<p>Question 2.<br \/>\n1.\\(\\overline { 27} \\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{28}{99}\\)<\/p>\n<p>Explanation:<br \/>\n1.\\(\\overline { 27} \\)<br \/>\nx = 1.\\(\\overline { 27} \\)<br \/>\n100x = 100(1.\\(\\overline { 27} \\))<br \/>\n100x = 127(\\(\\overline { 27} \\))<br \/>\nx = .\\(\\overline { 27} \\)<br \/>\n99x = 127<br \/>\nx = 127\/99<br \/>\nx = 1 28\/99<\/p>\n<p>Question 3.<br \/>\n1 \\(\\frac{7}{8}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n1.875<\/p>\n<p>Explanation:<br \/>\n1 \\(\\frac{7}{8}\\)<br \/>\n1 + 7\/8<br \/>\n8\/8 + 7\/8<br \/>\n15\/8 = 1.875<\/p>\n<p><strong>Solve each equation for x.<\/strong><\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> = 81<br \/>\n\u00b1 ______<\/p>\n<p>Answer:<br \/>\n\u00b1 9<\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> = 81<br \/>\nx = \u00b1 81<br \/>\nx = \u00b1 9<\/p>\n<p>Question 5.<br \/>\nx<sup>3<\/sup> = 343<br \/>\n______<\/p>\n<p>Answer:<br \/>\nx = 7<\/p>\n<p>Explanation:<br \/>\nx<sup>3<\/sup> = 343<br \/>\nx = 7<\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> = \\(\\frac{1}{100}\\)<br \/>\n\u00b1 \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\u00b1 \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> = \\(\\frac{1}{100}\\)<br \/>\nx = \u00b1 \\(\\frac{1}{10}\\)<\/p>\n<p>Question 7.<br \/>\nA square patio has an area of 200 square feet. How long is each side of the patio to the nearest 0.05?<br \/>\n______ feet<\/p>\n<p>Answer:<br \/>\n14.15 feet<\/p>\n<p>Explanation:<br \/>\nThe area of a square is found by multiplying the side of the square by itself. Therefore, to find the side of the square, we have to take the square root of the area.<br \/>\nLet&#8217;s denote with A the area of the patio and with s each side of the square.<br \/>\nWe have:<br \/>\nA = 200<br \/>\nA = s.s<br \/>\ns = \\(\\sqrt { A } \\) = \\(\\sqrt { 200 } \\)<br \/>\nFollowing the steps as in &#8220;Explore Activity&#8221; on page 9, we can make an estimation for the irrational number:<br \/>\n196 &lt; 200 &lt; 225<br \/>\n\\(\\sqrt { 196 } \\) &lt; \\(\\sqrt { 200 } \\) &lt; \\(\\sqrt { 225 } \\)<br \/>\n14 &lt; \\(\\sqrt { 200 } \\) &lt; 15<br \/>\nWe see that 200 is much closer to 196 than to 225, therefore the square root of it should be between 14 and 14.5. To make a better estimation, we pick some numbers between 14 and 14.5 and calculate their squares:<br \/>\n(14.1)\u00b2 = 198.81<br \/>\n(14.2)\u00b2 = 201.64<br \/>\n14.1 &lt; \\(\\sqrt { 200 } \\) &lt; 14.2<br \/>\n\\(\\sqrt { 200 } \\) = 14.15<br \/>\nWe see that 200 is much closer to 14.1 than to 14.2, therefore the square root of it should be between 14.1 and 14.15. If we round to the nearest 0.05, we have:<br \/>\ns = 14.15<\/p>\n<p><strong>1.2 Sets of Real Numbers<\/strong><\/p>\n<p><strong>Write all names that apply to each number.<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(\\frac { 121 }{ \\sqrt { 121 } }\\)<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nRational, whole, integer, real numbers<\/p>\n<p>Explanation:<br \/>\n\\(\\frac { 121 }{ \\sqrt { 121 } }\\)<br \/>\n121\/11 = 11<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{\u03c0}{2}\\)<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nIrrational, real numbers<\/p>\n<p>Question 10.<br \/>\nTell whether the statement \u201cAll integers are rational numbers\u201d is true or false. Explain your choice.<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nTrue<\/p>\n<p>Explanation:<br \/>\n\u201cAll integers are rational numbers\u201d is true, because every integer can be expressed as a fraction with a denominator equal to 1. The set of integer A a subset of rational numbers.<\/p>\n<p><strong>1.3 Ordering Real Numbers<\/strong><\/p>\n<p><strong>Compare. Write &lt;, &gt;, or =.<\/strong><\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt { 8 }\\) + 3 _______ 8 + \\(\\sqrt { 3 }\\)<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 8 }\\) + 3 &lt; 8 + \\(\\sqrt { 3 }\\)<\/p>\n<p>Explanation:<br \/>\n4 &lt; 8 &lt; 9<br \/>\n\\(\\sqrt { 4 }\\) &lt; \\(\\sqrt { 8 }\\) &lt; \\(\\sqrt { 9 }\\)<br \/>\n2 &lt; \\(\\sqrt { 8 }\\) &lt; 3<br \/>\n1 &lt; 3 &lt; 4<br \/>\n\\(\\sqrt { 1 }\\) &lt; \\(\\sqrt { 3 }\\) &lt; \\(\\sqrt { 4 }\\)<br \/>\n1 &lt; \\(\\sqrt { 3 }\\) &lt; 2<br \/>\n\\(\\sqrt { 8 }\\) + 3 is between 5 and 6<br \/>\n8 + \\(\\sqrt { 3 }\\) is between 9 and 10<br \/>\n\\(\\sqrt { 8 }\\) + 3 &lt; 8 + \\(\\sqrt { 3 }\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt { 5 }\\) + 11 _______ 5 + \\(\\sqrt { 11 }\\)<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { 5 }\\) + 11 &gt; 5 + \\(\\sqrt { 11 }\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 5 }\\) lies in between 2 and 3<br \/>\n\\(\\sqrt { 11 }\\) lies in between 3 and 4<br \/>\n\\(\\sqrt { 5 }\\) + 11 lies in between 13 and 14<br \/>\n5 + \\(\\sqrt { 11 }\\) lies in between 8 and 9<br \/>\n\\(\\sqrt { 5 }\\) + 11 &gt; 5 + \\(\\sqrt { 11 }\\)<\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt { 99 }\\), \u03c0<sup>2<\/sup>, 9.\\(\\bar { 8 }\\)<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n\u03c0<sup>2<\/sup>, 9.\\(\\bar { 8 }\\), \\(\\sqrt { 99 }\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { 99 }\\), \u03c0<sup>2<\/sup>, 9.\\(\\bar { 8 }\\)<br \/>\n99 lies between 9\u00b2 and 10\u00b2<br \/>\n99 is closer to 100, hence \\(\\sqrt { 99 }\\) is closer to 10<br \/>\n(9.9)\u00b2 = 98.01<br \/>\n(9.95)\u00b2 = 99.0025<br \/>\n(10)\u00b2 = 100<br \/>\n\\(\\sqrt { 99 }\\) = 9.95<br \/>\n\u03c0\u00b2 = 9.86<br \/>\n9.88888 = 9.89<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-8-300x52.png\" alt=\"grade 8 chapter 1 image 8\" width=\"300\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-8-300x52.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-8-768x134.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-8.png 780w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u03c0<sup>2<\/sup>, 9.\\(\\bar { 8 }\\), \\(\\sqrt { 99 }\\)<\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt { \\frac { 1 }{ 25 } } \\), \\(\\frac{1}{4}\\), 0.\\(\\bar { 2 }\\)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n\\(\\sqrt { \\frac { 1 }{ 25 } } \\), 0.\\(\\bar { 2 }\\), \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\sqrt { \\frac { 1 }{ 25 } } \\), \\(\\frac{1}{4}\\), 0.\\(\\bar { 2 }\\)<br \/>\n\\(\\sqrt { \\frac { 1 }{ 25 } } \\) = 1\/5 = 0.2<br \/>\n1\/4 = 0.25<br \/>\n0.\\(\\bar { 2 }\\) = 0.222 = 0.22<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-9-300x75.png\" alt=\"grade 8 chapter 1 image 9\" width=\"300\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-9-300x75.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-9.png 526w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\\(\\sqrt { \\frac { 1 }{ 25 } } \\), 0.\\(\\bar { 2 }\\), \\(\\frac{1}{4}\\)<\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 15.<br \/>\nHow are real numbers used to describe real-world situations?<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nIn real-world situations, we use real numbers to count or make measurements. They can be seen as a convention for us to quantify things around, for example, the distance, the temperature, the height, etc.<\/p>\n<h3><a id=\"Mixed_Review_-_Page_No._28\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 28<\/h3>\n<p>Question 1.<br \/>\nThe square root of a number is 9. What is the other square root?<br \/>\nOptions:<br \/>\na. -9<br \/>\nb. -3<br \/>\nc. 3<br \/>\nd. 81<\/p>\n<p>Answer:<br \/>\na. -9<\/p>\n<p>Explanation:<br \/>\nWe know that every positive number has two square roots, one positive and one negative. We are given the principal square root (9), so the other square root would be its negative (-9). To prove that, we square both numbers and we compare the results:<br \/>\n9 \u2022 9 = 81<br \/>\n(-9). (-9)= 81<\/p>\n<p>Question 2.<br \/>\nA square acre of land is 4,840 square yards. Between which two integers is the length of one side?<br \/>\nOptions:<br \/>\na. between 24 and 25 yards<br \/>\nb. between 69 and 70 yards<br \/>\nc. between 242 and 243 yards<br \/>\nd. between 695 and 696 yards<\/p>\n<p>Answer:<br \/>\nb. between 69 and 70 yards<\/p>\n<p>Explanation:<br \/>\nThe area of a square is found by multiplying the side of the square by itself. Therefore, to Bud the side of the square, we have to take the square root of the area.<br \/>\nLet&#8217;s denote with A the area of the land and with each side of the square. We have:<br \/>\nA = 4840<br \/>\nA = s . s<br \/>\nA = s\u00b2<br \/>\ns = \u221aA = \u221a4840<br \/>\nFollowing the steps as in \u00b0Explore Activity on page 9, we can make an estimation for the irrational number:<br \/>\n4761 &lt; 4840 &lt; 4900<br \/>\n\\(\\sqrt { 4761 }\\) &lt; \\(\\sqrt { 4840 }\\) &lt; \\(\\sqrt { 4900 }\\)<br \/>\n69 &lt; \\(\\sqrt { 4840 }\\) &lt; 70<br \/>\nEach side of the land is between 69 and 70 yards.<\/p>\n<p>Question 3.<br \/>\nWhich of the following is an integer but not a whole number?<br \/>\nOptions:<br \/>\na. -9.6<br \/>\nb. -4<br \/>\nc. 0<br \/>\nd. 3.7<\/p>\n<p>Answer:<br \/>\nb. -4<\/p>\n<p>Explanation:<br \/>\nWhole numbers are not negative<br \/>\n-4 is an integer but not a whole number<\/p>\n<p>Question 4.<br \/>\nWhich statement is false?<br \/>\nOptions:<br \/>\na. No integers are irrational numbers.<br \/>\nb. All whole numbers are integers.<br \/>\nc. No real numbers are irrational numbers.<br \/>\nd. All integers greater than 0 are whole numbers.<\/p>\n<p>Answer:<br \/>\nc. No real numbers are irrational numbers.<\/p>\n<p>Explanation:<br \/>\nRational and irrational numbers are real numbers.<\/p>\n<p>Question 5.<br \/>\nWhich set of numbers best describes the displayed weights on a digital scale that shows each weight to the nearest half pound?<br \/>\nOptions:<br \/>\na. whole numbers<br \/>\nb. rational numbers<br \/>\nc. real numbers<br \/>\nd. integers<\/p>\n<p>Answer:<br \/>\nb. rational numbers<\/p>\n<p>Explanation:<br \/>\nThe scale weighs nearest to 1\/2 pound.<\/p>\n<p>Question 6.<br \/>\nWhich of the following is <span style=\"text-decoration: underline;\">not<\/span> true?<br \/>\nOptions:<br \/>\na. \u03c0<sup>2<\/sup> &lt; 2\u03c0 + 4<br \/>\nb. 3\u03c0 &gt; 9<br \/>\nc. \\(\\sqrt { 27 }\\) + 3 &gt; 172<br \/>\nd. 5 \u2013 \\(\\sqrt { 24 }\\) &lt; 1<\/p>\n<p>Answer:<br \/>\nc. \\(\\sqrt { 27 }\\) + 3 &gt; 172<\/p>\n<p>Explanation:<br \/>\na. \u03c0<sup>2<\/sup> &lt; 2\u03c0 + 4<br \/>\n(3.14)\u00b2 &lt; 2(3.14) + 4<br \/>\n9.86 &lt; 10.28<br \/>\nTrue<br \/>\nb. 3\u03c0 &gt; 9<br \/>\n9.42 &gt; 9<br \/>\nTrue<br \/>\nc. \\(\\sqrt { 27 }\\) + 3 &gt; 172<br \/>\n5.2 + 3 &gt; 8.5<br \/>\n8.2 &gt; 8.5<br \/>\nFalse<br \/>\nd. 5 \u2013 \\(\\sqrt { 24 }\\) &lt; 1<br \/>\n5 &#8211; 4.90 &lt; 1<br \/>\n0.1 &lt; 1<br \/>\nTrue<\/p>\n<p>Question 7.<br \/>\nWhich number is between \\(\\sqrt { 21 }\\) and \\(\\frac{3\u03c0}{2}\\) ?<br \/>\nOptions:<br \/>\na. \\(\\frac{14}{3}\\)<br \/>\nb. 2 \\(\\sqrt { 6 }\\)<br \/>\nc. 5<br \/>\nd. \u03c0 + 1<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\na. \\(\\sqrt { 21 }\\) and \\(\\frac{3\u03c0}{2}\\)<br \/>\n\\(\\sqrt { 21 }\\) = 4.58<br \/>\n\\(\\frac{3\u03c0}{2}\\) = 4.71<br \/>\n14\/3 = 4.67<br \/>\nb. 2\\(\\sqrt { 6 }\\) = 4.90<br \/>\nc. 5<br \/>\nd. \u03c0 + 1 = 3.14 + 1 = 4.14<\/p>\n<p>Question 8.<br \/>\nWhat number is shown on the graph?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-1-Real-Numbers-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 1 Real Numbers Mixed Review img 11\" width=\"310\" height=\"52\" \/><br \/>\nOptions:<br \/>\na. \u03c0+3<br \/>\nb. \\(\\sqrt { 4 }\\) + 2.5<br \/>\nc. \\(\\sqrt { 20 }\\) + 2<br \/>\nd. 6.\\(\\overline { 14 } \\)<\/p>\n<p>Answer:<br \/>\nc. \\(\\sqrt { 20 }\\) + 2<\/p>\n<p>Explanation:<br \/>\n6.48<br \/>\na. \u03c0+3 = 3.14 + 3 = 6.14<br \/>\nb. \\(\\sqrt { 4 }\\) + 2.5 = 2 + 2.5 = 4.5<br \/>\nc. \\(\\sqrt { 20 }\\) + 2 = 4.47 + 2 = 6.47<br \/>\nd. 6.\\(\\overline { 14 } \\) = 6.1414<\/p>\n<p>Question 9.<br \/>\nWhich is in order from least to greatest?<br \/>\nOptions:<br \/>\na. 3.3, \\(\\frac{10}{3}\\), \u03c0, \\(\\frac{11}{4}\\)<br \/>\nb. \\(\\frac{10}{3}\\), 3.3, \\(\\frac{11}{4}\\), \u03c0<br \/>\nc. \u03c0, \\(\\frac{10}{3}\\), \\(\\frac{11}{4}\\), 3.3<br \/>\nd. \\(\\frac{11}{4}\\), \u03c0, 3.3, \\(\\frac{10}{3}\\)<\/p>\n<p>Answer:<br \/>\nd. \\(\\frac{11}{4}\\), \u03c0, 3.3, \\(\\frac{10}{3}\\)<\/p>\n<p>Explanation:<br \/>\n10\/3 = 3.3333333<br \/>\n11\/4 = 2.75<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-10-300x20.png\" alt=\"grade 8 chapter 1 image 10\" width=\"300\" height=\"20\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-10-300x20.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-10-768x52.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-1-image-10.png 900w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 10.<br \/>\nThe volume of a cube is given by V = x<sup>3<\/sup>, where x is the length of an edge of the cube. The area of a square is given by A = x<sup>2<\/sup>, where x is the length of a side of the square. A given cube has a volume of 1728 cubic inches.<br \/>\na. Find the length of an edge.<br \/>\n______ inches<\/p>\n<p>Answer:<br \/>\n12 inches<\/p>\n<p>Explanation:<br \/>\nV = x<sup>3<\/sup><br \/>\nA = x<sup>2<\/sup><br \/>\n1728 = x<sup>3<\/sup><br \/>\nx = 12<br \/>\nThe length of an edge = 12 in<\/p>\n<p>Question 10.<br \/>\nb. Find the area of one side of the cube.<br \/>\n______ in<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n144 in<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nA = (12)\u00b2 = 144<br \/>\nArea of the side of the cube = 144 in<sup>2<\/sup><\/p>\n<p>Question 10.<br \/>\nc. Find the surface area of the cube.<br \/>\n______ in<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n864 in<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nSA = 6 (12)\u00b2 = 864<br \/>\nThe surface area of the cube = 864 in<sup>2<\/sup><\/p>\n<p>Question 10.<br \/>\nd. What is the surface area in square feet?<br \/>\n______ ft<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n6 ft<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nSA = 864\/144 = 6<br \/>\nThe surface area of the cube = 6 ft<sup>2<\/sup><\/p>\n<h3>Conclusion:<\/h3>\n<p>We hope the details prevailed in this Grade 8 Go Math Answer Key Chapter 1 Real Numbers is helpful for you guys. Make use of the above links and try to solve all the problems. This HMH Go Math Grade 8 Answer Key also helps to complete the homework within the time without any mistakes. Stick to our ccssmathanswers.com site to get the pdf links of all the chapters. Feel free to post your comments in the below box. We will try to clarify your doubts as early as possible. All the Best Guys!!!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Solutions for Go Math Grade 8 Answer Key Chapter 1 Real Numbers are given in detail here. 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