{"id":6847,"date":"2014-03-25T16:20:56","date_gmt":"2014-03-25T16:20:56","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6847"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-introduction-to-solving-radical-equations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-introduction-to-solving-radical-equations\/","title":{"rendered":"Math Introduction to Solving Radical Equations"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

A radical equation is an equation that contains a radical that includes a variable.\u00a0 It is possible to solve many radical equations in two steps.\u00a0 However, it is important to check the solution in the original equation to make sure it checks, as it may not be a real solution.<\/p>\n

How Does a Radical Equation Work?<\/strong><\/p>\n

A radical equation is similar to any other type of equation, except that the variable is under the radical sign.\u00a0 The difference between the radical equation 3 + \u221ay = 6 and the equation 3 + x = 6 is an additional step, but the principle in solving both equations is the same.\u00a0 If \u221ay = 6 – 3, then \u221ay ) = 3.\u00a0 Similarly, if x = 6- 3, then x = 3.<\/p>\n

What Is the First Step in Solving a Radical Equation?<\/strong><\/p>\n

The first step in solving a radical equation is similar to the first step in solving any equation.\u00a0 Isolate the variable on one side of the equation by performing the operations needed.\u00a0 Suppose the equation were \u221ay +4 =12.\u00a0 In order to isolate the variable on the left side \u221ay + 4 – 4 = 12 – 4, or \u221ay = 9.\u00a0 Similarly, if the equation were 2\u221ax = 5, in order to isolate the variable on the left side, (2\u221ax)\/2 = 5\/2.<\/p>\n

What Happens Next?<\/strong><\/p>\n

After the variable has been isolated on the left side of the equation, then the radical can be solved.\u00a0 Since according to the definition (\u221ax)2<\/sup> = x for any positive number or 0, the radical can be eliminated by squaring both sides of the equation.\u00a0 Therefore, if \u221ay = 3, then y must equal 9, because the square root of 9 equals 3.\u00a0 Also, if \u221ax = 5\/2, then x = (5\/2)2<\/sup> or 25\/4.<\/p>\n

When Is a Solution not a Solution?<\/strong><\/p>\n

It is always important to check the solution in the original equation, because sometimes the \u201csolution\u201d doesn\u2019t fit.\u00a0 Suppose the equation is 5 + \u221ax = 3.\u00a0 According to the first step, \u221ax = 3 – 5 or \u221ax = -2.\u00a0 If both sides were squared, (\u221ax)2 <\/sup>=(-2)2<\/sup> or x would equal 4.\u00a0 However, 5 +\u221a4 equals 7 and 7 does not equal 3.\u00a0 There is not a way that x could equal both 7 and 3, so that problem has no solution.\u00a0 (Some textbooks call it an apparent solution, and others call it an extraneous solution.)<\/p>\n

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Overview: A radical equation is an equation that contains a radical that includes a variable.\u00a0 It is possible to solve many radical equations in two steps.\u00a0 However, it is important to check the solution in the original equation to make sure it checks, as it may not be a real solution. How Does a Radical […]<\/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":[2644,2645,2643],"class_list":["post-6847","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-apparent-solutions","tag-extraneous-solutions","tag-radical-equations"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6847","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=6847"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6847\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}