{"id":44305,"date":"2025-06-30T15:00:33","date_gmt":"2025-06-30T15:00:33","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=44305"},"modified":"2025-06-30T15:00:34","modified_gmt":"2025-06-30T15:00:34","slug":"how-do-you-simplify-the-square-root-of-180-and-how-do-you-know-that-it-is-in-the-simplest-form","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/how-do-you-simplify-the-square-root-of-180-and-how-do-you-know-that-it-is-in-the-simplest-form\/","title":{"rendered":"How do you simplify the square root of 180 and how do you know that it is in the simplest form"},"content":{"rendered":"\n<p>How do you simplify the square root of 180 and how do you know that it is in the simplest form<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To simplify the square root of 180, follow these steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Prime Factorization of 180<\/strong>:<br>First, break down 180 into its prime factors. Start by dividing 180 by the smallest prime number, which is 2: 180\u00f72=90\u21d2180=2\u00d790180 \\div 2 = 90 \\quad \\Rightarrow \\quad 180 = 2 \\times 90180\u00f72=90\u21d2180=2\u00d790 Next, divide 90 by 2 again: 90\u00f72=45\u21d2180=2\u00d72\u00d74590 \\div 2 = 45 \\quad \\Rightarrow \\quad 180 = 2 \\times 2 \\times 4590\u00f72=45\u21d2180=2\u00d72\u00d745 Now, divide 45 by 3, the next smallest prime number: 45\u00f73=15\u21d2180=2\u00d72\u00d73\u00d71545 \\div 3 = 15 \\quad \\Rightarrow \\quad 180 = 2 \\times 2 \\times 3 \\times 1545\u00f73=15\u21d2180=2\u00d72\u00d73\u00d715 Divide 15 by 3: 15\u00f73=5\u21d2180=2\u00d72\u00d73\u00d73\u00d7515 \\div 3 = 5 \\quad \\Rightarrow \\quad 180 = 2 \\times 2 \\times 3 \\times 3 \\times 515\u00f73=5\u21d2180=2\u00d72\u00d73\u00d73\u00d75 So, the prime factorization of 180 is: 180=22\u00d732\u00d75180 = 2^2 \\times 3^2 \\times 5180=22\u00d732\u00d75<\/li>\n\n\n\n<li><strong>Simplifying the Square Root<\/strong>:<br>When simplifying a square root, look for pairs of identical factors. If there is a pair, take one factor out of the square root. From the prime factorization 180=22\u00d732\u00d75180 = 2^2 \\times 3^2 \\times 5180=22\u00d732\u00d75, we have:<ul><li>A pair of 2&#8217;s (222^222)<\/li><li>A pair of 3&#8217;s (323^232)<\/li><\/ul>Each pair can be taken out of the square root as a single number. This means we can simplify the square root as follows: 180=22\u00d732\u00d75=22\u00d732\u00d75\\sqrt{180} = \\sqrt{2^2 \\times 3^2 \\times 5} = \\sqrt{2^2} \\times \\sqrt{3^2} \\times \\sqrt{5}180\u200b=22\u00d732\u00d75\u200b=22\u200b\u00d732\u200b\u00d75\u200b Since the square root of a square is just the number itself: 22=2,32=3\\sqrt{2^2} = 2, \\quad \\sqrt{3^2} = 322\u200b=2,32\u200b=3 So: 180=2\u00d73\u00d75=65\\sqrt{180} = 2 \\times 3 \\times \\sqrt{5} = 6\\sqrt{5}180\u200b=2\u00d73\u00d75\u200b=65\u200b<\/li>\n\n\n\n<li><strong>Verifying the Simplest Form<\/strong>:<br>A square root is in its simplest form when no perfect square factors other than 1 are left inside the radical. In this case, 5 is not a perfect square, and there are no further simplifications. Therefore, the square root of 180 in its simplest form is 656\\sqrt{5}65\u200b.<\/li>\n<\/ol>\n\n\n\n<p>Thus, the square root of 180 simplifies to 656\\sqrt{5}65\u200b, and it is in its simplest form because no further simplifications are possible.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1492.jpeg\" alt=\"\" class=\"wp-image-44316\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1492.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1492-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1492-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>How do you simplify the square root of 180 and how do you know that it is in the simplest form The Correct Answer and Explanation is: To simplify the square root of 180, follow these steps: Thus, the square root of 180 simplifies to 656\\sqrt{5}65\u200b, and it is in its simplest form because no [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-44305","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44305","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=44305"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44305\/revisions"}],"predecessor-version":[{"id":44317,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44305\/revisions\/44317"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=44305"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=44305"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=44305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}