{"id":222708,"date":"2025-05-31T16:43:46","date_gmt":"2025-05-31T16:43:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222708"},"modified":"2025-05-31T16:43:48","modified_gmt":"2025-05-31T16:43:48","slug":"combine-these-radicals-6a%cb%86s100-a%cb%86s36-a-66-b-54-c-6a%cb%86s136-d-6a%cb%86s16-please-help","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/31\/combine-these-radicals-6a%cb%86s100-a%cb%86s36-a-66-b-54-c-6a%cb%86s136-d-6a%cb%86s16-please-help\/","title":{"rendered":"Combine these radicals: -6\u00e2\u02c6\u0161100 + \u00e2\u02c6\u016136 A. -66 B. -54 C. -6\u00e2\u02c6\u0161136 D. -6\u00e2\u02c6\u016116 Please help!!"},"content":{"rendered":"\n
Combine these radicals: -6\u00e2\u02c6\u0161100 + \u00e2\u02c6\u016136 A. -66 B. -54 C. -6\u00e2\u02c6\u0161136 D. -6\u00e2\u02c6\u016116 Please help!! Combine these radicals: -6\u00e2\u02c6\u0161100 + \u00e2\u02c6\u016136 A. -66 B. -54 C. -6\u00e2\u02c6\u0161136 D. -6\u00e2\u02c6\u016116 Please help!!<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Let’s first simplify the expression step by step:<\/p>\n\n\n\n
Now substitute the simplified values: \u22126\u22c510+6=\u221260+6=\u221254-6 \\cdot 10 + 6 = -60 + 6 = -54<\/p>\n\n\n\n
\u2705 Final Answer: B. -54<\/strong><\/h3>\n\n\n\n\n\n\n\n
\ud83d\udd0d Explanation <\/h3>\n\n\n\n
Radicals, also known as square roots, represent the inverse operation of squaring a number. To simplify expressions involving radicals, we must first simplify each square root and then apply any coefficients or operations.<\/p>\n\n\n\n
In the expression \u22126100+36-6\\sqrt{100} + \\sqrt{36}, we are dealing with two radicals that involve perfect squares.<\/p>\n\n\n\n
Start by simplifying each square root:<\/p>\n\n\n\n
\n
100\\sqrt{100} equals 10 because 102=10010^2 = 100.<\/li>\n\n\n\n
36\\sqrt{36} equals 6 because 62=366^2 = 36.<\/li>\n<\/ul>\n\n\n\n
Now apply the coefficient of -6 to 100\\sqrt{100}:<\/p>\n\n\n\n
This gives us the final result: -54<\/strong><\/p>\n\n\n\n
It is important to note that we do not combine radicals directly unless they are like radicals<\/strong>, meaning they have the same value inside the square root. For example, 23+53=732\\sqrt{3} + 5\\sqrt{3} = 7\\sqrt{3}, but 2+3\\sqrt{2} + \\sqrt{3} cannot be simplified further.<\/p>\n\n\n\n
In this case, we were lucky because both numbers inside the radicals\u2014100 and 36\u2014are perfect squares. That means their square roots are integers (10 and 6, respectively), which makes the computation straightforward.<\/p>\n\n\n\n
This question tests two key skills:<\/p>\n\n\n\n
\n
Knowing how to simplify perfect square roots.<\/li>\n\n\n\n
Applying arithmetic operations (multiplication and addition) properly once radicals are simplified.<\/li>\n<\/ol>\n\n\n\n
Answer choice B, -54<\/strong>, is correct.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Combine these radicals: -6\u00e2\u02c6\u0161100 + \u00e2\u02c6\u016136 A. -66 B. -54 C. -6\u00e2\u02c6\u0161136 D. -6\u00e2\u02c6\u016116 Please help!!Combine these radicals: -6\u00e2\u02c6\u0161100 + \u00e2\u02c6\u016136 A. -66 B. -54 C. -6\u00e2\u02c6\u0161136 D. -6\u00e2\u02c6\u016116 Please help!! The Correct Answer and Explanation is: Let’s first simplify the expression step by step: Given expression: \u22126100+36-6\\sqrt{100} + \\sqrt{36} Step 1: Simplify 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-222708","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222708","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=222708"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222708\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222708"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222708"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222708"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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