Between which two numbers does \u221a72 lie on a number line?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find between which two numbers ( \\sqrt{72} ) lies on a number line, we begin by simplifying the square root.<\/p>\n\n\n\n Start by factoring 72 into its prime factors:<\/p>\n\n\n\n [ Since ( \\sqrt{36} = 6 ), we can simplify the square root as follows:<\/p>\n\n\n\n [ Now we need to estimate ( \\sqrt{2} ). ( \\sqrt{2} ) is approximately 1.414. Thus:<\/p>\n\n\n\n [ To determine between which two whole numbers ( \\sqrt{72} ) lies, we can use the fact that:<\/p>\n\n\n\n Since ( \\sqrt{72} ) is between the squares of 8 and 9, we conclude that:<\/p>\n\n\n\n [ Thus, ( \\sqrt{72} ) lies between 8 and 9 on the number line.<\/p>\n\n\n\n We started by simplifying ( \\sqrt{72} ) and approximating the value of ( \\sqrt{2} ), which gave us 8.484. This value is greater than 8 but less than 9. The square roots of perfect squares, such as ( \\sqrt{64} = 8 ) and ( \\sqrt{81} = 9 ), help us place ( \\sqrt{72} ) between these two values. This process shows how approximations and properties of square roots can be used to estimate where a number lies on a number line.<\/p>\n","protected":false},"excerpt":{"rendered":" Between which two numbers does \u221a72 lie on a number line? The Correct Answer and Explanation is : To find between which two numbers ( \\sqrt{72} ) lies on a number line, we begin by simplifying the square root. Step 1: Simplify ( \\sqrt{72} ) Start by factoring 72 into its prime factors: [72 = […]<\/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-164078","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164078","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=164078"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164078\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=164078"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=164078"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=164078"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Simplify ( \\sqrt{72} )<\/h3>\n\n\n\n
72 = 36 \\times 2
]<\/p>\n\n\n\n
\\sqrt{72} = \\sqrt{36 \\times 2} = \\sqrt{36} \\times \\sqrt{2} = 6 \\times \\sqrt{2}
]<\/p>\n\n\n\n
\\sqrt{72} = 6 \\times 1.414 \\approx 8.484
]<\/p>\n\n\n\nStep 2: Identify the two numbers on the number line<\/h3>\n\n\n\n
\n
8 < \\sqrt{72} < 9
]<\/p>\n\n\n\nStep 3: Understanding the reasoning<\/h3>\n\n\n\n