{"id":224013,"date":"2025-06-02T15:51:59","date_gmt":"2025-06-02T15:51:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224013"},"modified":"2025-06-02T15:52:01","modified_gmt":"2025-06-02T15:52:01","slug":"evaluate-the-square-root-25-144-25-144","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/evaluate-the-square-root-25-144-25-144\/","title":{"rendered":"Evaluate the square root 25 144 25 144"},"content":{"rendered":"\n

Evaluate the square root 25 144 25 144 (Simplify your answer )<\/p>\n\n\n\n

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

To evaluate the square root of the expression 25 144 25 144<\/strong>, we first need to understand how it is written. If the numbers are simply written together without mathematical symbols, we assume it’s a multiplication: 25\u00d7144\u00d725\u00d7144\\sqrt{25 \\times 144 \\times 25 \\times 144}<\/p>\n\n\n\n

Step-by-step Evaluation:<\/h3>\n\n\n\n
    \n
  1. Group and simplify<\/strong>: (25\u00d725)\u00d7(144\u00d7144)=252\u00d71442\\sqrt{(25 \\times 25) \\times (144 \\times 144)} = \\sqrt{25^2 \\times 144^2}<\/li>\n\n\n\n
  2. Use exponent rules<\/strong>: (25\u00d7144)2\\sqrt{(25 \\times 144)^2}<\/li>\n\n\n\n
  3. Simplify square root<\/strong>: (25\u00d7144)2=25\u00d7144\\sqrt{(25 \\times 144)^2} = 25 \\times 144<\/li>\n\n\n\n
  4. Multiply<\/strong>: 25\u00d7144=360025 \\times 144 = 3600<\/li>\n<\/ol>\n\n\n\n

    \u2705 Final Answer:<\/h3>\n\n\n\n

    3600\\boxed{3600}<\/p>\n\n\n\n

    \n\n\n\n

    \u2728 Explanation <\/h3>\n\n\n\n

    This problem involves simplifying a square root expression that initially seems complex due to its format. The key is recognizing patterns and applying properties of square roots and exponents.<\/p>\n\n\n\n

    We begin with the expression: 25\u00d7144\u00d725\u00d7144\\sqrt{25 \\times 144 \\times 25 \\times 144}<\/p>\n\n\n\n

    Notice that 25 appears twice, and 144 appears twice. We can group them using exponent notation: 252\u00d71442\\sqrt{25^2 \\times 144^2}<\/p>\n\n\n\n

    Now, apply the property of square roots: a2\u00d7b2=(a\u00d7b)2\\sqrt{a^2 \\times b^2} = \\sqrt{(a \\times b)^2}<\/p>\n\n\n\n

    This simplifies our expression to: (25\u00d7144)2\\sqrt{(25 \\times 144)^2}<\/p>\n\n\n\n

    The square root of a square cancels out the square root and the exponent: x2=x\\sqrt{x^2} = x<\/p>\n\n\n\n

    So, (25\u00d7144)2=25\u00d7144\\sqrt{(25 \\times 144)^2} = 25 \\times 144<\/p>\n\n\n\n

    Now we perform the multiplication: 25\u00d7144=(25\u00d7100)+(25\u00d744)=2500+1100=360025 \\times 144 = (25 \\times 100) + (25 \\times 44) = 2500 + 1100 = 3600<\/p>\n\n\n\n

    Thus, the square root simplifies to 3600<\/strong>.<\/p>\n\n\n\n

    This process demonstrates how recognizing patterns, applying exponent rules, and using arithmetic efficiently leads to a simplified answer. Simplifying under the square root by identifying perfect squares and factoring is a common and helpful method in algebra and helps avoid complex calculations or guesswork.<\/p>\n\n\n\n

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

    Evaluate the square root 25 144 25 144 (Simplify your answer ) The Correct Answer and Explanation is: To evaluate the square root of the expression 25 144 25 144, we first need to understand how it is written. If the numbers are simply written together without mathematical symbols, we assume it’s a multiplication: 25\u00d7144\u00d725\u00d7144\\sqrt{25 […]<\/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-224013","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224013","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=224013"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224013\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224013"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224013"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}