What the square root of 243<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The square root of 243 is approximately 15.588<\/strong>.<\/p>\n\n\n\n To find the square root of 243, you are essentially looking for a number that, when multiplied by itself, equals 243. In mathematical terms, if we let ( x ) represent the square root of 243, then:<\/p>\n\n\n\n [ To simplify square roots, a common method is using prime factorization. This means breaking down 243 into its prime factors.<\/p>\n\n\n\n So, the prime factorization of 243 is:<\/p>\n\n\n\n [ Now that we have ( 243 = 3^5 ), we can apply the rule for square roots. When dealing with square roots, any factor that appears in pairs can be taken out of the square root.<\/p>\n\n\n\n Here, ( 3^5 ) contains two pairs of 3\u2019s: Thus, ( \\sqrt{243} = 9 \\sqrt{3} ).<\/p>\n\n\n\n Now, let\u2019s estimate ( \\sqrt{3} ). The square root of 3 is approximately 1.732, so:<\/p>\n\n\n\n [ The square root of 243, simplified, is ( 9 \\sqrt{3} ), and the decimal approximation is about 15.588<\/strong>. This approach shows how prime factorization helps simplify square roots and gives both an exact and approximate answer.<\/p>\n","protected":false},"excerpt":{"rendered":" What the square root of 243 The Correct Answer and Explanation is: The square root of 243 is approximately 15.588. Explanation: To find the square root of 243, you are essentially looking for a number that, when multiplied by itself, equals 243. In mathematical terms, if we let ( x ) represent the square root […]<\/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-157575","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157575","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=157575"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157575\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=157575"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=157575"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=157575"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
x^2 = 243
]<\/p>\n\n\n\nPrime Factorization Method:<\/h3>\n\n\n\n
\n
\n
243 = 3 \\times 3 \\times 3 \\times 3 \\times 3 = 3^5
]<\/p>\n\n\n\nSimplifying the Square Root:<\/h3>\n\n\n\n
[
3^5 = 3^2 \\times 3^2 \\times 3
]
Since ( \\sqrt{3^2} = 3 ), we can simplify this as:
[
\\sqrt{243} = \\sqrt{3^2 \\times 3^2 \\times 3} = 3 \\times 3 \\times \\sqrt{3} = 9 \\sqrt{3}
]<\/p>\n\n\n\nApproximation:<\/h3>\n\n\n\n
9 \\times \\sqrt{3} \\approx 9 \\times 1.732 = 15.588
]<\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n