{"id":168023,"date":"2024-11-16T16:25:45","date_gmt":"2024-11-16T16:25:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168023"},"modified":"2024-11-16T16:25:47","modified_gmt":"2024-11-16T16:25:47","slug":"determine-which-two-values-the-following-expression-is-between","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/16\/determine-which-two-values-the-following-expression-is-between\/","title":{"rendered":"Determine which two values the following expression is between."},"content":{"rendered":"\n<p>Determine which two values the following expression is between.<br>\u221a37<\/p>\n\n\n\n<p>A. 7 and 8<br>B. 5 and 6<br>C. 4 and 5<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine which two values the square root of (37) ((\\sqrt{37})) lies between, let\u2019s first identify the perfect squares closest to (37):<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(6^2 = 36)<\/li>\n\n\n\n<li>(7^2 = 49)<\/li>\n<\/ol>\n\n\n\n<p>Thus, (36 &lt; 37 &lt; 49). This means (\\sqrt{37}) is greater than (6) but less than (7), so the correct answer is:<br><strong>A. 7 and 8<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The square root function identifies a number that, when squared, equals the given value. For example, (\\sqrt{36} = 6) because (6^2 = 36), and (\\sqrt{49} = 7) because (7^2 = 49). For non-perfect squares, such as (37), the square root will be a decimal between the square roots of the two nearest perfect squares.<\/p>\n\n\n\n<p>Here\u2019s why (\\sqrt{37}) lies between (6) and (7):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(6^2 = 36), which is less than (37), so (\\sqrt{37} > 6).<\/li>\n\n\n\n<li>(7^2 = 49), which is greater than (37), so (\\sqrt{37} &lt; 7).<\/li>\n<\/ul>\n\n\n\n<p>Since (37) is just slightly larger than (36), (\\sqrt{37}) will be slightly greater than (6). Performing a rough estimation:<br>[<br>\\sqrt{37} \\approx 6.08<br>]<br>This confirms that it falls between (6) and (7).<\/p>\n\n\n\n<p>If you were to test the other options:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Option <strong>B<\/strong>: (5) and (6): (\\sqrt{37}) cannot fit here because (37 > 36) ((6^2)), and (\\sqrt{37} > 6).<\/li>\n\n\n\n<li>Option <strong>C<\/strong>: (4) and (5): This is even less plausible, as (37) is much larger than (25) ((5^2)).<\/li>\n<\/ul>\n\n\n\n<p>Thus, the answer is <strong>A. 6 and 7<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determine which two values the following expression is between.\u221a37 A. 7 and 8B. 5 and 6C. 4 and 5 The Correct Answer and Explanation is: To determine which two values the square root of (37) ((\\sqrt{37})) lies between, let\u2019s first identify the perfect squares closest to (37): Thus, (36 &lt; 37 &lt; 49). This means [&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-168023","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168023","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=168023"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168023\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168023"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168023"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168023"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}