{"id":6639,"date":"2014-01-09T18:11:14","date_gmt":"2014-01-09T18:11:14","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6639"},"modified":"2014-12-02T08:26:54","modified_gmt":"2014-12-02T08:26:54","slug":"math-review-of-simplifying-radicals","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-simplifying-radicals\/","title":{"rendered":"Math Review of Simplifying Radicals"},"content":{"rendered":"<p><strong>Overview:<\/strong><\/p>\n<p>Before many operations can be performed with expressions involving radicals, the radicals must be simplified.\u00a0 This ensures that they are factored so that there are no perfect square factors under the radical sign.\u00a0 Approximations of the nonnegative square root can then be calculated.<\/p>\n<p><strong>How Are Radicals Factored?<\/strong><\/p>\n<p>The process of factoring radicals is similar to factoring other numbers. For example, a number such as \u221a400 can be simplified to the rational number 20, because 20 times 20 = 400.\u00a0 It could also be factored as \u221a4\u221a100, because both 4 and 100 are factors of 400.\u00a0 In this example, the square root of 4 is 2 and the square root of 100 is 10 and 2 \u2219 10 equals 20.\u00a0 Speaking algebraically, if a and b are real numbers greater than or equal to zero, then \u221aab = \u221aa\u221ab.<\/p>\n<p><strong>Finding Perfect Squares<\/strong><\/p>\n<p>Using the algebraic definition, the radical can be broken down into parts that are easier to solve.\u00a0 For example, the square root of 50 equals \u221a25\u221a2, or 5\u221a2.\u00a0 Similarly, an expression such as 3\u221a8 can be simplified as (3)\u221a4\u221a2, or 3\u22192\u221a2 or 6\u221a2.\u00a0 The important thing is to find the largest possible perfect square and another factor, then solve.<\/p>\n<p><strong>What About Variables?<\/strong><\/p>\n<p>The exponents for variables can be factored using the rules of exponents.\u00a0 Suppose the expression is \u221a4d<sup>5<\/sup>.\u00a0 It can be factored as \u221a4\u221ad<sup>5<\/sup>, or 2\u221ad<sup>5<\/sup>, but the variable \u221ad<sup>5<\/sup> is not in its simplest terms.\u00a0 The variable \u221ad<sup>5<\/sup> can be expressed as 2d<sup>2<\/sup>\u221ad.<\/p>\n<p><strong>What About Combinations of Variables and Numbers?<\/strong><\/p>\n<p>To factor expressions that combine more than one variable, each variable can be simplified to find the largest possible perfect square, then combined in steps.\u00a0 Suppose the expression is \u221a144a<sup>9<\/sup>b<sup>2<\/sup>. \u00a0It can be factored as \u221a144\u221aa<sup>9<\/sup>\u221ab<sup>2<\/sup>.\u00a0 The square root of 144 is 12, the square root of a<sup>9<\/sup> is \u221aa<sup>8<\/sup>\u2219\u221aa or a<sup>4<\/sup>\u221aa, and the square root of b<sup>2<\/sup> is b.\u00a0 Putting it all together, the simplified expression is 12ba<sup>4<\/sup>\u221aa.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/algebra-tutoring\/\">algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n<p><span class=\"tutorOrange\">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 Olympia, WA visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-olympia-washington\/\">Tutoring in Olympia, WA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview: Before many operations can be performed with expressions involving radicals, the radicals must be simplified.\u00a0 This ensures that they are factored so that there are no perfect square factors under the radical sign.\u00a0 Approximations of the nonnegative square root can then be calculated. How Are Radicals Factored? The process of factoring radicals is similar [&hellip;]<\/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":[645,1312,1645],"class_list":["post-6639","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-factoring","tag-perfect-squares","tag-simplifying-radicals"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6639","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=6639"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6639\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}