{"id":7203,"date":"2014-06-30T16:20:19","date_gmt":"2014-06-30T16:20:19","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=7203"},"modified":"2014-12-02T08:25:28","modified_gmt":"2014-12-02T08:25:28","slug":"math-review-of-the-square-root-property","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-the-square-root-property\/","title":{"rendered":"Math Review of the Square Root Property"},"content":{"rendered":"

Overview<\/h3>\n

The square root property is an important shortcut to use when solving quadratic equations, or any equation that asks for square roots and powers of 2. It uses the definition of a square root to solve for a variable.<\/p>\n

Definition<\/h3>\n

The definition of the square root of a positive real number in symbol form is if x2<\/sup> = a, then x = \u00b1\u221aa. For example, the square root of 64 is \u00b18, because 8\u22198 is 64 and -8\u2219-8 is also 64. Suppose that y2<\/sup> = b. Using substitution, y = \u00b1\u221ab. The variable b can stand for a positive real number, a monomial, or even a polynomial.<\/p>\n

Using the Square Root Property with Positive Real Numbers<\/h3>\n

Suppose that x2<\/sup> = 100. Then x will equal \u00b1\u221a100, or 10 or -10. Suppose that y2<\/sup> + 11 = 92. Then y2<\/sup> = 92 – 11. If y2<\/sup> = 81, then y will equal \u00b1\u221a81, or 9 or -9. Suppose that x2<\/sup> = 49\/25. Then x will equal \u221a(49\/25) or \u00b17\/5.<\/p>\n

Figure 1: The square root property holds with positive real numbers and variables.<\/p>\n

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

Using the Square Root Property with Monomials<\/h3>\n

The square root property can also be used with monomials. Suppose the equation is 36x4<\/sup>y2<\/sup> = z2<\/sup>. Using the square root property, z equals \u221a(36x4<\/sup>y2<\/sup>) or 6x2<\/sup>y, because the square root of 36 is 6, the square root of x4<\/sup> is x2<\/sup> and the square root of y2<\/sup> is y. Similarly, if q2<\/sup> equals 20a4<\/sup>b2<\/sup> then q will equal 2 a2<\/sup>b\u221a5. This is because the square root of 20 equals 2\u221a5, the square root of a4<\/sup> is a2<\/sup> and the square root of b2<\/sup> is b.<\/p>\n

Figure 2: The process of using the square root property with a monomial.<\/p>\n

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

Using the Square Root Property with Quadratic Equations<\/h3>\n

Using the square root property can be a shortcut to solving perfect square trinomials. Suppose the equation is x2<\/sup> + 6x + 9 = 36. In this case, both sides are perfect squares, because the perfect square trinomial is (x +3)2<\/sup> = 62<\/sup>. Therefore x + 3 = \u00b16. Solving for x + 3 = 6, x = 6 -3 or 3. Solving for x + 3 = -6, x = -6 – 3, or -9.<\/p>\n

Figure 3: Using the square root property to solve a quadratic equation.<\/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 Moose Jaw, SK, Canada: visit Tutoring in Moose Jaw, SK, Canada<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview The square root property is an important shortcut to use when solving quadratic equations, or any equation that asks for square roots and powers of 2. It uses the definition of a square root to solve for a variable. Definition The definition of the square root of a positive real number in symbol form […]<\/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":[1146,2749,1456,2748],"class_list":["post-7203","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-monomials","tag-positive-real-numbers","tag-quadratic-equations","tag-square-root-property"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7203","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=7203"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7203\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=7203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=7203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=7203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}