{"id":149295,"date":"2024-10-07T07:23:51","date_gmt":"2024-10-07T07:23:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=149295"},"modified":"2024-10-07T07:23:54","modified_gmt":"2024-10-07T07:23:54","slug":"which-two-numbers-does-the-square-root-of-128-lie-between-on-a-number-line","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/07\/which-two-numbers-does-the-square-root-of-128-lie-between-on-a-number-line\/","title":{"rendered":"Which two numbers does the square root of 128 lie between on a number line"},"content":{"rendered":"\n<p>Which two numbers does the square root of 128 lie between on a number line<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is:<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-3-color\"><strong> 11.312<\/strong><\/mark><\/p>\n\n\n\n<p>To determine which two numbers the square root of 128 lies between, we can start by estimating the square root.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Calculating Square Root<\/strong>:<br>[<br>\\sqrt{128}<br>]<\/li>\n\n\n\n<li><strong>Finding Perfect Squares<\/strong>:<br>We need to find two perfect squares that are closest to 128:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(11^2 = 121)<\/li>\n\n\n\n<li>(12^2 = 144) Since (121 &lt; 128 &lt; 144), it follows that:<br>[<br>11 &lt; \\sqrt{128} &lt; 12<br>]<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Estimating More Accurately<\/strong>:<br>To get a more accurate estimate of (\\sqrt{128}), we can calculate it:<br>[<br>\\sqrt{128} = \\sqrt{64 \\times 2} = \\sqrt{64} \\cdot \\sqrt{2} = 8 \\cdot \\sqrt{2}<br>]<br>The approximate value of (\\sqrt{2}) is about (1.414), thus:<br>[<br>8 \\cdot 1.414 \\approx 11.312<br>]<\/li>\n<\/ol>\n\n\n\n<p>This calculation confirms that (\\sqrt{128} \\approx 11.312).<\/p>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li><strong>Conclusion<\/strong>:<br>The square root of 128 lies between 11 and 12. More specifically, it is closer to 11.3, confirming that:<br>[<br>11 &lt; \\sqrt{128} &lt; 12<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Understanding square roots is fundamental in mathematics, particularly in geometry and algebra. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, determining the square root of 128 helps us locate its value on a number line.<\/p>\n\n\n\n<p>When estimating square roots, identifying perfect squares allows us to create bounds. Perfect squares are integers that result from squaring whole numbers. Since (11^2) and (12^2) bracket 128, we can confidently state that the square root of 128 falls between these two integers.<\/p>\n\n\n\n<p>Calculating the square root more precisely reveals that (\\sqrt{128}) is approximately 11.312. This approximation helps visualize where the value lies on the number line, further reinforcing the conclusion that the square root of 128 is indeed between 11 and 12.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which two numbers does the square root of 128 lie between on a number line The Correct Answer and Explanation is : The correct answer is: 11.312 To determine which two numbers the square root of 128 lies between, we can start by estimating the square root. This calculation confirms that (\\sqrt{128} \\approx 11.312). Explanation: [&hellip;]<\/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-149295","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149295","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=149295"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149295\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}