{"id":256446,"date":"2025-07-16T09:30:26","date_gmt":"2025-07-16T09:30:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256446"},"modified":"2025-07-16T09:30:29","modified_gmt":"2025-07-16T09:30:29","slug":"the-following-calculations-are-all-wrong-please-explain-whats-gone-wrong-and-what-is-the-correct-way-to-calculate-them-square-root-of-2-cross-times-cube-root-of-4-space-equals-cube-root-of-2-cross","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/the-following-calculations-are-all-wrong-please-explain-whats-gone-wrong-and-what-is-the-correct-way-to-calculate-them-square-root-of-2-cross-times-cube-root-of-4-space-equals-cube-root-of-2-cross\/","title":{"rendered":"The following calculations are all wrong, please explain what’s gone wrong and what is the correct way to calculate them square root of 2 cross times cube root of 4 space equals cube root of 2 cross times 4 end root equals cube root of 8 square root of 4 plus 16 end root space equals space square root of 4 plus square root of 16 equals 2 plus 4 equals 6 2 square root of 3 plus 7 square root of 3 space equals left parenthesis 2 plus 7 right parenthesis square root of 3 plus 3 end root equals 9 square root of 6"},"content":{"rendered":"\n
The following calculations are all wrong, please explain what’s gone wrong and what is the correct way to calculate them square root of 2 cross times cube root of 4 space equals cube root of 2 cross times 4 end root equals cube root of 8 square root of 4 plus 16 end root space equals space square root of 4 plus square root of 16 equals 2 plus 4 equals 6 2 square root of 3 plus 7 square root of 3 space equals left parenthesis 2 plus 7 right parenthesis square root of 3 plus 3 end root equals 9 square root of 6<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Let us go through each calculation and identify the mistakes, then explain the correct method and results.<\/p>\n\n\n\n
But then you incorrectly added \u221b3 and somehow got 9\u221a6<\/li>\n\n\n\n
You cannot combine square roots and cube roots this way<\/li>\n<\/ul>\n\n\n\n
Correct calculation:<\/strong><\/p>\n\n\n\n
\n
2\u221a3 + 7\u221a3 = 9\u221a3<\/li>\n\n\n\n
If \u221b3 is separate, it stays separate unless there’s a reason to combine<\/li>\n\n\n\n
There\u2019s no valid algebraic operation that turns 9\u221a3 + \u221b3 into 9\u221a6<\/li>\n<\/ul>\n\n\n\n\n\n\n\n
Summary<\/h3>\n\n\n\n
The major mistakes here involve:<\/p>\n\n\n\n
\n
Misapplying rules of radicals (roots cannot be combined across types)<\/li>\n\n\n\n
Incorrect distribution of roots over addition<\/li>\n\n\n\n
Trying to simplify expressions where no simplification is possible<\/li>\n<\/ul>\n\n\n\n
Correct approach:<\/strong><\/p>\n\n\n\n
\n
Keep square roots and cube roots separate unless all terms are the same type<\/li>\n\n\n\n
Only combine like radicals (same root and same radicand)<\/li>\n\n\n\n
Use properties of exponents and radicals correctly: \u221aa \u00d7 \u221ab = \u221a(a \u00d7 b) only<\/strong> if both are square roots But \u221aa \u00d7 \u221bb cannot be simplified into one root<\/li>\n<\/ul>\n\n\n\n
Accurate simplification requires following these algebraic rules carefully.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
The following calculations are all wrong, please explain what’s gone wrong and what is the correct way to calculate them square root of 2 cross times cube root of 4 space equals cube root of 2 cross times 4 end root equals cube root of 8 square root of 4 plus 16 end root space […]<\/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-256446","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256446","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=256446"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256446\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256446"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256446"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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