find the root of 1152 by using prime factorisation ?<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To find the square root of 1152 using prime factorization, we start by breaking 1152 down into its prime factors.<\/p>\n\n\n\n First, we divide 1152 by the smallest prime number, which is 2.<\/p>\n\n\n\n 1152 \u00f7 2 = 576 Now, 9 is not divisible by 2, so we move to the next prime number, which is 3.<\/p>\n\n\n\n 9 \u00f7 3 = 3 So, the prime factorization of 1152 is: To take the square root of a number using prime factorization, we use the property that the square root of a product is the product of the square roots of the factors.<\/p>\n\n\n\n The square root of a number is found by dividing the powers of the prime factors by 2, since we are looking for pairs of primes.<\/p>\n\n\n\n For 1152 = 2\u2077 \u00d7 3\u00b2, the square root is calculated as: Since \u221a2 is approximately 1.414, the square root of 1152 is: Thus, the square root of 1152 is approximately 33.94.<\/p>\n\n\n\n The exact square root is 8\u221a2, but an approximate value is 33.94. This method of prime factorization helps break down the number into its prime components, making it easier to handle square roots, especially with non-perfect squares.<\/p>\n","protected":false},"excerpt":{"rendered":" find the root of 1152 by using prime factorisation ? The correct answer and explanation is: To find the square root of 1152 using prime factorization, we start by breaking 1152 down into its prime factors. Step 1: Prime Factorization of 1152 First, we divide 1152 by the smallest prime number, which is 2. 1152 […]<\/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-259182","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259182","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=259182"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259182\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259182"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Prime Factorization of 1152<\/h3>\n\n\n\n
576 \u00f7 2 = 288
288 \u00f7 2 = 144
144 \u00f7 2 = 72
72 \u00f7 2 = 36
36 \u00f7 2 = 18
18 \u00f7 2 = 9<\/p>\n\n\n\n
3 \u00f7 3 = 1<\/p>\n\n\n\n
1152 = 2\u2077 \u00d7 3\u00b2<\/p>\n\n\n\nStep 2: Taking the Square Root<\/h3>\n\n\n\n
\u221a1152 = \u221a(2\u2077 \u00d7 3\u00b2)
= 2^(7\/2) \u00d7 3^(2\/2)
= 2\u00b3 \u00d7 2^(1\/2) \u00d7 3
= 8 \u00d7 \u221a2 \u00d7 3<\/p>\n\n\n\nStep 3: Approximation<\/h3>\n\n\n\n
\u221a1152 \u2248 8 \u00d7 1.414 \u00d7 3
\u2248 8 \u00d7 4.242
\u2248 33.936<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n