{"id":7214,"date":"2014-07-03T17:42:28","date_gmt":"2014-07-03T17:42:28","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=7214"},"modified":"2014-12-02T08:25:28","modified_gmt":"2014-12-02T08:25:28","slug":"math-review-of-multiplying-and-simplifying-radical-expressions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-multiplying-and-simplifying-radical-expressions\/","title":{"rendered":"Math Review of Multiplying and Simplifying Radical Expressions"},"content":{"rendered":"

Overview<\/h3>\n

Radical expressions contain one or more radicands, or expressions underneath root signs.\u00a0They can be multiplied following rules for non-negative real numbers.<\/p>\n

Radical Expressions<\/h3>\n

Radical expressions that do not have variables, such as \u221a9 or \u221a25 or even 6\u221a5 are already familiar.\u00a0 The radicand can also be a monomial, such as \u221a(9x2<\/sup>) or over a polynomial, such as \u221a(x2<\/sup> + 14x + 49).\u00a0 Suppose the radical expression were \u221a64.\u00a0 The equivalent is the number 8, because 8 is the square root of 64.\u00a0 Similarly, if the expression contained a variable, such as \u221ax4<\/sup>, its equivalent would be x2<\/sup>, because x2<\/sup> is the square root of x4<\/sup>.<\/p>\n

Figure 1:\u00a0 The radicand can be a monomial.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Multiplying Radical Expressions<\/h3>\n

Radical expressions can be multiplied as long as they are non-negative real numbers.\u00a0 In symbol form, \u221aa \u2219 \u221ab equals \u221aab.\u00a0 For example, \u221a16 \u2219 \u221a25 is the same thing as \u221a (16 \u2219 25) or \u221a400.\u00a0 This can be checked because \u221a16 equals 4 and \u221a25 equals 5 and 4 times 5 is 20, the square root of 400.\u00a0 Similarly, \u221a81 \u2219 \u221ax6<\/sup> equals \u221a (81x6<\/sup>) or 9x3<\/sup> because \u221a81 is 9 and \u221ax6<\/sup> is x3<\/sup>, and 9 times x3 <\/sup>equals 9x3<\/sup>.\u00a0Also, \u221a(x + 2) \u2219 \u221a(x – 2) equals \u221a(x + 2)(x – 2) or \u221a(x2<\/sup> – 4).<\/p>\n

Factoring Radical Expressions<\/h3>\n

Factoring radical expressions is also possible as long as the numbers are non-negative real numbers, such that \u221aab equals \u221aa \u2219 \u221ab.\u00a0 For example, \u221a(100a10<\/sup>) is the same thing as \u221a100 \u2219 \u221aa10<\/sup>.\u00a0 Similarly, \u221a(x2<\/sup> – 12x + 36) is the same thing as \u221a(x – 6)(x – 6).<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

Simplifying Radical Expressions<\/h3>\n

Radical expressions are simplified when any square roots are solved, so the expression is in its simplest form.\u00a0 For example, \u221a(100a18<\/sup>) can be simplified as 10a9<\/sup> because both factors are perfect squares.\u00a0 The square root of a18<\/sup> is a9<\/sup>, using the rules of exponents, because a18<\/sup> = a9 + 9<\/sup>.\u00a0 Similarly, \u221a(b2<\/sup> +22b + 121) can be simplified to (b + 11) because (b + 11)(b + 11) equals b2<\/sup> + 22b + 121. However, \u221a(x2<\/sup> – 4) is already in its simplest form, as it is factored to \u221a(x + 2)(x \u2013 2).\u00a0 The sum of square roots is not the same thing as the product of square roots.\u00a0 For example, \u221a(16 + 9) equals \u221a25 which is 5.\u00a0 However, the square root of 16 is 4 and the square root of 9 is 3 is 7, and 7 does not equal 5.<\/p>\n

Figure 3:\u00a0 The sum of square roots is not the same thing as the product of square roots.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

\"monohybridcross\"<\/a><\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Ketchikan, AK: visit Tutoring in Ketchikan, AK<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Radical expressions contain one or more radicands, or expressions underneath root signs.\u00a0They can be multiplied following rules for non-negative real numbers. Radical Expressions Radical expressions that do not have variables, such as \u221a9 or \u221a25 or even 6\u221a5 are already familiar.\u00a0 The radicand can also be a monomial, such as \u221a(9×2) or over a […]<\/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":[2753,2752,1644],"class_list":["post-7214","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-factoring-radical-expressions","tag-multiplying-radical-expressions","tag-simplifying-radical-expressions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7214","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=7214"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7214\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=7214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=7214"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=7214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}