{"id":6645,"date":"2014-01-18T17:15:29","date_gmt":"2014-01-18T17:15:29","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6645"},"modified":"2014-12-02T08:26:54","modified_gmt":"2014-12-02T08:26:54","slug":"multiplication-and-division-of-radicals","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/multiplication-and-division-of-radicals\/","title":{"rendered":"Multiplication and Division of Radicals"},"content":{"rendered":"

Overview:<\/strong>
\nMultiplication and division of radicals use the same properties as other types of multiplication.\u00a0 It is much easier to simplify expressions before they are used in an expression.\u00a0 Also, the result needs to be checked carefully to make sure the expression is in its simplest form.<\/p>\n

Factoring a Radical<\/strong>
\nMultiplying a radical is defined algebraically as \u221aab = \u221aa\u221ab.\u00a0 This definition is very helpful when multiplying two radicals.\u00a0 For example, suppose the problem is -(\u221a6)\u2219(\u221a3).\u00a0 That is equal to \u221a18, which can further be simplified to 3\u221a2.\u00a0 There are actually two ways to do this, and both arrive at the same answer.\u00a0 One way is to think of \u221a6 as being factored further as \u221a2\u221a3 and multiply by \u221a3.\u00a0 Now, \u221a3 times itself by definition equals 3, and then multiply by \u221a2, so the simplest form of\u221a18 is 3\u221a2.\u00a0 The other way is to think of \u221a18 as \u221a9\u221a2 and then solve as 3\u221a2.\u00a0 The first way illustrates the concept of what a square root means, that \u221aa \u2219\u221aa is the same thing as a.<\/p>\n

Using the Commutative and Associative Properties<\/strong>
\nSuppose the number is -3\u221a6 \u2219 4\u221a3.\u00a0 It can be solved by moving the factors around and associating them, as all the operations to be performed are multiplication. \u00a0\u00a0\u00a0\u00a0This rewrites the problem to \u00a0(-3\u2219 4)(\u221a6\u221a3) or -12(\u221a18), which can be further simplified to -12 \u22193\u221a2 or -36\u221a2.<\/p>\n

Division of Radicals<\/strong>
\nThe definition of division of radicals is similar to the definition of multiplication of radicals.\u00a0 If a and b are real numbers, neither are negative, and b is not equal to zero, then \u221a(a\/b) is the same thing as \u221aa\/\u221ab.\u00a0 It can also be shown by using real numbers as examples.\u00a0 For example, \u221a(9\/25) is simplified completely as 3\/5.\u00a0 Similarly, \u221a9\/\u221a25 is also simplified as 3\/5.<\/p>\n

Rationalizing the Denominator<\/strong>
\nIn order for the numerator to be in simplest terms, all perfect squares should be factored out from under the radical.\u00a0 In addition, the denominator of the fraction should not contain any radicals either.\u00a0 Suppose the final expression was \u221a2\/\u221a5.\u00a0 In order to eliminate the \u221a5 in the denominator, multiply the expression by \u221a5\/\u221a5.\u00a0 The numerator will be \u221a2\u221a5 and the denominator of the fraction will be 5.\u00a0 The resulting fraction (\u221a2\u221a5)\/5 is in simplest terms.<\/p>\n

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Overview: Multiplication and division of radicals use the same properties as other types of multiplication.\u00a0 It is much easier to simplify expressions before they are used in an expression.\u00a0 Also, the result needs to be checked carefully to make sure the expression is in its simplest form. Factoring a Radical Multiplying a radical is defined […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[531,1160,1493],"class_list":["post-6645","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-division-of-radicals","tag-multiplication-of-radicals","tag-rationalizing-the-denominator"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6645","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6645"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6645\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6645"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6645"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6645"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}