{"id":49286,"date":"2023-10-28T11:42:51","date_gmt":"2023-10-28T06:12:51","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=49286"},"modified":"2023-11-10T12:09:59","modified_gmt":"2023-11-10T06:39:59","slug":"perfect-square-or-square-number","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/perfect-square-or-square-number\/","title":{"rendered":"Perfect Square or Square Number Definition, Examples | How to find the Perfect Square of a Number?"},"content":{"rendered":"

A Perfect Square is formed by squaring a whole number. For example 1\u00b2 = 1; 2\u00b2 = 4; 3\u00b2 = 9; 4\u00b2 = 16; 5\u00b2 = 25 and so on. Thus 1, 4, 9, 16, 25, etc., are perfect squares. Learn complete information regarding the perfect square<\/a> and how to find it in this article. We have given examples and also their explanations to understand it easily. Therefore, it is now your part to begin practice and get a complete grip on the concept.<\/p>\n

Examples:
\n1 = 1\u00b2; 4 = 2\u00b2; 9 = 3\u00b2; 16 = 4\u00b2; 25 = 5\u00b2 and so on. Here 1, 4, 9, 16, 25, etc., are perfect squares.<\/p>\n

How to Find a Perfect Square or Square Number?<\/h2>\n

A perfect square number is defined as the product of pairs of equal factors. Or it can also express as grouped in pairs of equal factors.<\/p>\n

1. Find out if the following numbers are perfect squares?
\n(i) 169
\n(ii) 512
\n(iii) 64<\/p>\n

Solution:
\n(i) Given number is 169
\nFind the prime factors of the given number 169.
\nThe prime factors of 169 are 13 and 13.
\nGrouping the factors into the pairs of equal factors.
\n(13 \u00d7 13)
\nFactors of the 169 are 13 \u00d7 13.<\/p>\n

Therefore, 169 is a perfect square.<\/p>\n

(ii) Given number is 512
\nFind the prime factors of the given number 512.
\nThe prime factors of 169 are 8, 8, and 8.
\nGrouping the factors into the pairs of equal factors.
\n(8 \u00d7 8) \u00d7 8
\nFactors of the 169 are 8 \u00d7 8 \u00d7 8.
\n8 is not grouped in pairs of equal factors.<\/p>\n

Therefore, 512 is not a perfect square.<\/p>\n

(iii) Given number is 64
\nFind the prime factors of the given number 64.
\nThe prime factors of 64 are 8, and 8.
\nGrouping the factors into the pairs of equal factors.
\n(8 \u00d7 8)
\nFactors of the 169 are 8 \u00d7 8.<\/p>\n

Therefore, 64 is a perfect square.<\/p>\n

2. Is 16 a perfect square? If so, find the number whose square is 16.<\/p>\n

Solution:
\nGiven number is 16
\nFind the prime factors of the given number 16.
\nThe prime factors of 16 are 2, 2, 2, and 2.
\nGrouping the factors into the pairs of equal factors.
\n(2 \u00d7 2) \u00d7(2 \u00d7 2)
\nTherefore, 16 is a perfect square.
\nTake one number from each group and multiply them to find the number whose square is 16.
\n2 \u00d7 2 = 4.<\/p>\n

4 is the number whose square is 16.<\/p>\n

3. Is 576 a perfect square? If so, find the number whose square is 576.<\/p>\n

Solution:
\nGiven number is 576
\nFind the prime factors of the given number 16.
\nThe prime factors of 16 are 2, 2, 3, 3, 4, and 4.
\nGrouping the factors into the pairs of equal factors.
\n(2 \u00d7 2) \u00d7 (3 \u00d7 3) \u00d7 (4 \u00d7 4)
\nTherefore, 576 is a perfect square.
\nTake one number from each group and multiply them to find the number whose square is 576.
\n2 \u00d7 3 \u00d7 4 = 24.<\/p>\n

24 is the number whose square is 576.<\/p>\n

4. Show that 288 is not a perfect square.<\/p>\n

Solution:
\nGiven number is 288
\nFind the prime factors of the given number 288.
\nThe prime factors of 16 are 2, 3, 3, 4, and 4.
\nGrouping the factors into the pairs of equal factors.
\n2 \u00d7 (3 \u00d7 3) \u00d7 (4 \u00d7 4)
\n2 is not grouped in pairs of equal factors.<\/p>\n

Therefore, 288 is not a perfect square.<\/p>\n

5. Find the smallest number by which 100 must be multiplied to make it a perfect square?<\/p>\n

Solution:
\nThe given number is 100.
\nFind the prime factors of the given number 100.
\nThe prime factors of 100 are 5, 5, and 4.
\nGrouping the factors into the pairs of equal factors.
\n4 \u00d7 (5 \u00d7 5)
\n4 is not grouped in pairs of equal factors.
\nTherefore, by multiplying 4 to 100, we make 100 as a perfect square.<\/p>\n

4 is the smallest number by which 100 must be multiplied to make it a perfect square<\/p>\n

6. Find the smallest number by which 180 must be divided so as to get a perfect square.<\/p>\n

Solution:
\nThe given number is 180.
\nFind the prime factors of the given number 180.
\nThe prime factors of 180 are 2, 2, 3, 3, and 5.
\nGrouping the factors into the pairs of equal factors.
\n5 \u00d7 (3 \u00d7 3) \u00d7 (2 \u00d7 2)
\n5 is not grouped in pairs of equal factors.
\nTherefore, by dividing 5 by 180, we make 180 a perfect square.<\/p>\n

5 is the smallest number by which 180 must be divided so as to get a perfect square.<\/p>\n","protected":false},"excerpt":{"rendered":"

A Perfect Square is formed by squaring a whole number. For example 1\u00b2 = 1; 2\u00b2 = 4; 3\u00b2 = 9; 4\u00b2 = 16; 5\u00b2 = 25 and so on. Thus 1, 4, 9, 16, 25, etc., are perfect squares. Learn complete information regarding the perfect square and how to find it in this article. … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/49286"}],"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\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=49286"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/49286\/revisions"}],"predecessor-version":[{"id":92564,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/49286\/revisions\/92564"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=49286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=49286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=49286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}