{"id":162168,"date":"2024-11-06T09:31:13","date_gmt":"2024-11-06T09:31:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=162168"},"modified":"2024-11-06T09:31:15","modified_gmt":"2024-11-06T09:31:15","slug":"find-the-two-whole-numbers-that-are-the-closest-to-%e2%88%9a42","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/06\/find-the-two-whole-numbers-that-are-the-closest-to-%e2%88%9a42\/","title":{"rendered":"Find the two whole numbers that are the closest to \u221a42."},"content":{"rendered":"\n

Find the two whole numbers that are the closest to \u221a42.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the two whole numbers that are closest to ( \\sqrt{42} ), let’s first estimate the square root of 42 and then determine which whole numbers are nearest.<\/p>\n\n\n\n

Step 1: Understanding square roots<\/h3>\n\n\n\n

The square root of a number ( n ) is the number that, when multiplied by itself, gives ( n ). In mathematical terms:<\/p>\n\n\n\n

[
\\sqrt{n} = x \\quad \\text{where} \\quad x^2 = n.
]<\/p>\n\n\n\n

We are asked to find the square root of 42, so we need to determine which two whole numbers ( x ) and ( x+1 ) (or ( x-1 )) are closest to ( \\sqrt{42} ).<\/p>\n\n\n\n

Step 2: Estimating ( \\sqrt{42} )<\/h3>\n\n\n\n

We know that ( 6^2 = 36 ) and ( 7^2 = 49 ). Since ( 42 ) is between these two perfect squares, ( \\sqrt{42} ) must be between 6 and 7.<\/p>\n\n\n\n

To be more precise, we can estimate:<\/p>\n\n\n\n

    \n
  • ( 6.5^2 = 6.5 \\times 6.5 = 42.25 )<\/li>\n\n\n\n
  • ( 6.4^2 = 6.4 \\times 6.4 = 40.96 )<\/li>\n<\/ul>\n\n\n\n

    The square of 6.5 is 42.25, which is very close to 42, and the square of 6.4 is 40.96, which is a little lower. Therefore, we can conclude that ( \\sqrt{42} ) is slightly less than 6.5.<\/p>\n\n\n\n

    Step 3: Closest whole numbers<\/h3>\n\n\n\n

    Since ( \\sqrt{42} ) is between 6 and 7, and it is closer to 6.5 than to 7, we can say that the two whole numbers closest to ( \\sqrt{42} ) are 6 and 7.<\/p>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    The two whole numbers closest to ( \\sqrt{42} ) are 6 and 7<\/strong>.<\/p>\n\n\n\n

    This estimation technique helps us find the closest whole numbers without using a calculator. The process involves comparing the square of different numbers to find the range in which the square root lies.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Find the two whole numbers that are the closest to \u221a42. The Correct Answer and Explanation is: To find the two whole numbers that are closest to ( \\sqrt{42} ), let’s first estimate the square root of 42 and then determine which whole numbers are nearest. Step 1: Understanding square roots The square root of […]<\/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-162168","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162168","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=162168"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162168\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=162168"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=162168"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=162168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}