{"id":6398,"date":"2013-10-21T14:53:53","date_gmt":"2013-10-21T14:53:53","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6398"},"modified":"2014-12-02T08:26:57","modified_gmt":"2014-12-02T08:26:57","slug":"math-review-of-radical-expressions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/10\/21\/math-review-of-radical-expressions\/","title":{"rendered":"Math Review of Radical Expressions"},"content":{"rendered":"

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

Radical expressions involving square roots have many applications in algebra.\u00a0 If an equation calls for a variable to be squared, its solution will be a square root.\u00a0 The principal square root is a positive number.<\/p>\n

What Are Perfect Squares?<\/strong><\/p>\n

Perfect squares have whole numbers as square roots.\u00a0 For example, \u221a9 equals 3, and \u221a16 equals 4.\u00a0 That is because 32<\/sup>=9 and 42<\/sup>=16.\u00a0 In addition, both 9 and 16 have negative square roots, -3 and -4, but they are not usually considered. Sometimes perfect squares can be found by prime factorizations.\u00a0 For example, 576 can be factored as 26\u2219<\/sup>\u2219 32<\/sup>.\u00a0 The square root of 26<\/sup> is 23<\/sup>, because 23<\/sup>\u221923<\/sup> is 26<\/sup>, and the square root of 32<\/sup> is 3.\u00a0 The square root of 576 is then 8 \u2219 3, or 24.<\/p>\n

What Are Irrational Numbers?<\/strong><\/p>\n

Most numbers, however, are not perfect squares.\u00a0 For example, what is \u221a10?\u00a0 Prime factorization will not help in this case, because neither \u221a5 or\u221a2 are perfect squares.\u00a0 The \u221a10 is approximately 3.16227766, and the decimal neither repeats or terminates.\u00a0 Decimals that neither repeat or terminate are irrational numbers, because there is no fraction that exactly expresses them.<\/p>\n

When Are Radical Expressions in Simplest Form?<\/strong><\/p>\n

Radical expressions are in simplest form if all perfect square factors other than 1 have been simplified.\u00a0 According to the Product Property of Square Roots, \u221aab = \u221aa\u2219\u221ab for any numbers a and b when both a and b are greater than zero.\u00a0 Therefore, \u221a20 can be simplified to \u221a4\u2219\u221a5, or 2\u221a5.\u00a0 Similarly, \u221a20\u2219\u221a10 can be simplified to \u221a10\u221910\u22192 or 10\u221a2.<\/p>\n

How to Add or Subtract Radical Expressions?<\/strong><\/p>\n

In order to add or subtract radical expressions, the radicands (the numbers under the radical sign) must be alike and in simplest form.\u00a0 For example, 9\u221a7-4\u221a2 + 3\u221a2 + 5\u221a7 can be simplified using the commutative property to 14\u221a7-\u221a2.\u00a0 Suppose the expression was 3\u221a20 + 4\u221a5 + 5\u221a3.\u00a0 It could be simplified to 3( 2\u221a5) + 4\u221a5 + 5\u221a3 or 6\u221a5 + 4\u221a5 + 5\u221a3 or 10\u221a5 + 5\u221a3.<\/p>\n

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Overview Radical expressions involving square roots have many applications in algebra.\u00a0 If an equation calls for a variable to be squared, its solution will be a square root.\u00a0 The principal square root is a positive number. What Are Perfect Squares? Perfect squares have whole numbers as square roots.\u00a0 For example, \u221a9 equals 3, and \u221a16 […]<\/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":[48,1644,1760],"class_list":["post-6398","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-adding-radical-expressions","tag-simplifying-radical-expressions","tag-subtracting-radical-expressions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6398"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6398\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}