Square root of 75 simplified<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: (5\\sqrt{3})<\/strong><\/mark><\/p>\n\n\n\n To simplify the square root of 75, we break it down into its prime factors:<\/p>\n\n\n\n [ Next, we use the fact that the square root of a product is the product of the square roots:<\/p>\n\n\n\n [ Since (\\sqrt{25} = 5), we get:<\/p>\n\n\n\n [ Thus, the simplified form of (\\sqrt{75}) is (5\\sqrt{3}).<\/p>\n\n\n\n The goal of simplifying square roots is to express them in a form that contains the smallest possible radical. For (\\sqrt{75}), we first need to break 75 into its prime factors. Prime factorization helps us identify perfect squares, which can be simplified.<\/p>\n\n\n\n The number 75 can be factored as:<\/p>\n\n\n\n [ Here, 25 is a perfect square, and (\\sqrt{25}) is 5. This allows us to simplify the square root of the product. The square root of 75 then becomes:<\/p>\n\n\n\n [ The square root of 3 remains under the radical because 3 is a prime number and cannot be simplified further. So, the expression (5\\sqrt{3}) is the simplest form of (\\sqrt{75}).<\/p>\n\n\n\n This process of simplifying square roots by factoring out perfect squares is a common technique in algebra. It makes calculations easier and expressions neater, especially when dealing with irrational numbers, like the square root of 3, which cannot be simplified into a whole number.<\/p>\n","protected":false},"excerpt":{"rendered":" Square root of 75 simplified The Correct Answer and Explanation is : The correct answer is: (5\\sqrt{3}) To simplify the square root of 75, we break it down into its prime factors: [\\sqrt{75} = \\sqrt{25 \\times 3}] Next, we use the fact that the square root of a product is the product of the square […]<\/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-150017","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150017","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=150017"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150017\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\sqrt{75} = \\sqrt{25 \\times 3}
]<\/p>\n\n\n\n
\\sqrt{75} = \\sqrt{25} \\times \\sqrt{3}
]<\/p>\n\n\n\n
\\sqrt{75} = 5\\sqrt{3}
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n
75 = 25 \\times 3
]<\/p>\n\n\n\n
\\sqrt{75} = 5\\sqrt{3}
]<\/p>\n\n\n\n