{"id":228656,"date":"2025-06-07T12:59:01","date_gmt":"2025-06-07T12:59:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228656"},"modified":"2025-06-07T12:59:04","modified_gmt":"2025-06-07T12:59:04","slug":"what-is-the-simplified-form-of-square-root-of-45","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/what-is-the-simplified-form-of-square-root-of-45\/","title":{"rendered":"What is the simplified form of square root of 45"},"content":{"rendered":"\n

What is the simplified form of square root of 45<\/p>\n\n\n\n

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

Simplified Form of \u221a45:<\/strong><\/h3>\n\n\n\n

45=35\\sqrt{45} = 3\\sqrt{5}45\u200b=35\u200b<\/p>\n\n\n\n

\n\n\n\n

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

To simplify the square root of 45, we need to break it down into its prime factors and look for perfect squares.<\/p>\n\n\n\n

Step 1: Prime Factorization of 45<\/strong><\/h4>\n\n\n\n

We start by factoring 45:45=9\u00d7545 = 9 \\times 545=9\u00d75<\/p>\n\n\n\n

Here, 9 is a perfect square because:9=3\u00d73=329 = 3 \\times 3 = 3^29=3\u00d73=32<\/p>\n\n\n\n

So, we can rewrite the square root as:45=9\u00d75\\sqrt{45} = \\sqrt{9 \\times 5}45\u200b=9\u00d75\u200b<\/p>\n\n\n\n

Step 2: Use the Property of Square Roots<\/strong><\/h4>\n\n\n\n

One of the main properties of square roots is:a\u00d7b=a\u00d7b\\sqrt{a \\times b} = \\sqrt{a} \\times \\sqrt{b}a\u00d7b\u200b=a\u200b\u00d7b\u200b<\/p>\n\n\n\n

Applying this:45=9\u00d75\\sqrt{45} = \\sqrt{9} \\times \\sqrt{5}45\u200b=9\u200b\u00d75\u200b<\/p>\n\n\n\n

Since 9=3\\sqrt{9} = 39\u200b=3, we get:45=35\\sqrt{45} = 3\\sqrt{5}45\u200b=35\u200b<\/p>\n\n\n\n

This is the simplified form<\/strong> of the square root of 45. It cannot be simplified further because 5 is a prime number<\/strong> and not a perfect square.<\/p>\n\n\n\n

\n\n\n\n

Why Simplification Matters<\/strong><\/h3>\n\n\n\n

Simplifying square roots helps in:<\/p>\n\n\n\n

    \n
  • Solving algebraic equations<\/li>\n\n\n\n
  • Reducing complexity in math expressions<\/li>\n\n\n\n
  • Understanding irrational numbers more clearly<\/li>\n<\/ul>\n\n\n\n

    In this case, 45\u22486.708\\sqrt{45} \\approx 6.70845\u200b\u22486.708, but 353\\sqrt{5}35\u200b is a more exact form<\/strong>, especially useful in algebra and geometry where precision is key.<\/p>\n\n\n\n

    \n\n\n\n

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

    45=35\\boxed{\\sqrt{45} = 3\\sqrt{5}}45\u200b=35\u200b\u200b<\/p>\n\n\n\n

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

    What is the simplified form of square root of 45 The Correct Answer and Explanation is: Simplified Form of \u221a45: 45=35\\sqrt{45} = 3\\sqrt{5}45\u200b=35\u200b Explanation To simplify the square root of 45, we need to break it down into its prime factors and look for perfect squares. Step 1: Prime Factorization of 45 We start by […]<\/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-228656","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228656","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=228656"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228656\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228656"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228656"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228656"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}