What is the square root of 52 simplified?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To simplify the square root of 52, we first break down the number into its prime factors and then simplify the square root expression.<\/p>\n\n\n\n The first step is to find the prime factorization of 52. We divide 52 by the smallest prime numbers:<\/p>\n\n\n\n [ Thus, the prime factorization of 52 is: Now, we take the square root of 52. We can express the square root as follows: Since the square root of (2^2) is 2, we get: Thus, the simplified form of the square root of 52 is: This is the simplest form of the square root of 52. We cannot simplify (\\sqrt{13}) further, as 13 is a prime number and does not have a square root that simplifies into an integer.<\/p>\n\n\n\n The process of simplifying square roots involves finding the prime factors of the number under the root, grouping factors into pairs (because the square root of a pair of identical factors simplifies to a whole number), and pulling these out of the square root. For 52, we recognized that (2^2) forms a pair, allowing us to take 2 out of the square root, leaving (\\sqrt{13}), which cannot be simplified further. This method ensures that the square root is expressed in its simplest form.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the square root of 52 simplified? The Correct Answer and Explanation is: To simplify the square root of 52, we first break down the number into its prime factors and then simplify the square root expression. Step 1: Factorization of 52 The first step is to find the prime factorization of 52. We […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-167114","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167114","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=167114"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167114\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Factorization of 52<\/h3>\n\n\n\n
52 \\div 2 = 26 \\quad \\text{(since 52 is even, we divide by 2)}
]
[
26 \\div 2 = 13 \\quad \\text{(26 is also even, so divide by 2 again)}
]
[
13 \\div 13 = 1 \\quad \\text{(13 is a prime number, so we stop here)}
]<\/p>\n\n\n\n
[
52 = 2 \\times 2 \\times 13 = 2^2 \\times 13
]<\/p>\n\n\n\nStep 2: Simplifying the Square Root<\/h3>\n\n\n\n
[
\\sqrt{52} = \\sqrt{2^2 \\times 13}
]
Using the property of square roots, (\\sqrt{a \\times b} = \\sqrt{a} \\times \\sqrt{b}), we separate the square root into two parts:
[
\\sqrt{52} = \\sqrt{2^2} \\times \\sqrt{13}
]<\/p>\n\n\n\n
[
\\sqrt{52} = 2 \\times \\sqrt{13}
]<\/p>\n\n\n\nStep 3: Final Answer<\/h3>\n\n\n\n
[
\\sqrt{52} = 2\\sqrt{13}
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n