Approximate square root of 53 to the nearest integer.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: 7<\/strong><\/mark><\/p>\n\n\n\n To approximate the square root of 53 to the nearest integer, we begin by recognizing that the square root of a number ( n ) is the value ( x ) such that ( x^2 = n ). In this case, we are looking for ( \\sqrt{53} ).<\/p>\n\n\n\n First, we need to identify two perfect squares between which 53 lies. The perfect square just below 53 is ( 49 ) (which is ( 7^2 )), and the perfect square just above it is ( 64 ) (which is ( 8^2 )). Thus, we can deduce:<\/p>\n\n\n\n [ Next, we can refine our approximation by calculating ( 7.5^2 ) to see if it is closer to 53:<\/p>\n\n\n\n [ Since ( 56.25 ) is greater than ( 53 ), this tells us that ( \\sqrt{53} ) is less than ( 7.5 ). To narrow it down further, we can try ( 7.2 ) and ( 7.3 ):<\/p>\n\n\n\n Calculating ( 7.2^2 ):<\/p>\n\n\n\n [ And calculating ( 7.3^2 ):<\/p>\n\n\n\n [ From these calculations, we find that:<\/p>\n\n\n\n [ Since ( 7.2 ) is just below and ( 7.3 ) is just above 53, we can conclude that ( \\sqrt{53} ) is approximately ( 7.28 ) when calculated more precisely. However, since we are looking for the nearest integer, we see that ( 7.28 ) rounds up to ( 7 ).<\/p>\n\n\n\n Thus, the square root of 53, rounded to the nearest integer, is:<\/p>\n\n\n\n [ This approximation demonstrates an essential mathematical skill: estimating square roots by comparing with known perfect squares and refining guesses through simple calculations.<\/p>\n","protected":false},"excerpt":{"rendered":" Approximate square root of 53 to the nearest integer. The Correct Answer and Explanation is : The correct answer is: 7 To approximate the square root of 53 to the nearest integer, we begin by recognizing that the square root of a number ( n ) is the value ( x ) such that ( […]<\/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-150777","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150777","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=150777"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150777\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
7^2 < 53 < 8^2 \\quad \\Rightarrow \\quad 7 < \\sqrt{53} < 8
]<\/p>\n\n\n\n
7.5^2 = 56.25
]<\/p>\n\n\n\n
7.2^2 = 51.84
]<\/p>\n\n\n\n
7.3^2 = 53.29
]<\/p>\n\n\n\n
51.84 < 53 < 53.29 \\quad \\Rightarrow \\quad 7.2 < \\sqrt{53} < 7.3
]<\/p>\n\n\n\n
\\boxed{7}
]<\/p>\n\n\n\n