{"id":223838,"date":"2025-06-02T12:02:51","date_gmt":"2025-06-02T12:02:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223838"},"modified":"2025-06-02T12:02:53","modified_gmt":"2025-06-02T12:02:53","slug":"estimate-the-value-of-the-following-to-the-nearest-to-one-decimal-place-of-%e2%88%9a150","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/estimate-the-value-of-the-following-to-the-nearest-to-one-decimal-place-of-%e2%88%9a150\/","title":{"rendered":"Estimate the value of the following to the nearest to one decimal place of \u221a150"},"content":{"rendered":"\n

Estimate the value of the following to the nearest to one decimal place of \u221a150<\/p>\n\n\n\n

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

The square root of 150, to one decimal place, is:<\/p>\n\n\n\n

\u221a150 \u2248 12.2<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

To estimate the square root of 150, we are trying to find a number which, when multiplied by itself, gives a value close to 150. This process is useful in mathematics and science when working with measurements, geometry, and real-world applications that require approximations.<\/p>\n\n\n\n

First, let\u2019s find two perfect squares that 150 lies between:<\/p>\n\n\n\n

    \n
  • 144=12\\sqrt{144} = 12 (since 122=14412^2 = 144)<\/li>\n\n\n\n
  • 169=13\\sqrt{169} = 13 (since 132=16913^2 = 169)<\/li>\n<\/ul>\n\n\n\n

    So, 150\\sqrt{150} is between 12 and 13. Now, we can narrow it down:<\/p>\n\n\n\n

    Try 12.212.2:
    12.2\u00d712.2=148.8412.2 \\times 12.2 = 148.84<\/p>\n\n\n\n

    Try 12.312.3:
    12.3\u00d712.3=151.2912.3 \\times 12.3 = 151.29<\/p>\n\n\n\n

    Since 150 is between 148.84 and 151.29, we see that 12.2 is closer to \u221a150<\/strong> than 12.3 is. Therefore, to one decimal place:<\/p>\n\n\n\n

    \u221a150 \u2248 12.2<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Why Estimating Square Roots Matters<\/h3>\n\n\n\n

    In many real-life scenarios, especially when using calculators isn’t allowed or when precision is flexible, estimating square roots helps us understand the scale or size of a value. Engineers, scientists, and students often estimate square roots to quickly analyze data or check for calculation errors.<\/p>\n\n\n\n

    This method of approximation is also a stepping stone to more advanced topics like solving quadratic equations, understanding irrational numbers, and using number sense. In fact, the square root of 150 is an irrational number<\/strong>, which means it has an infinite number of non-repeating decimal places and cannot be expressed exactly as a fraction.<\/p>\n\n\n\n

    In conclusion, estimating \u221a150 gives us a value of 12.2<\/strong> to one decimal place, which is a practical and useful approximation in many contexts.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Estimate the value of the following to the nearest to one decimal place of \u221a150 The Correct Answer and Explanation is: The square root of 150, to one decimal place, is: \u221a150 \u2248 12.2 Explanation To estimate the square root of 150, we are trying to find a number which, when multiplied by itself, gives […]<\/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-223838","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223838","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=223838"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223838\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223838"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223838"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}