{"id":6636,"date":"2014-01-01T18:51:32","date_gmt":"2014-01-01T18:51:32","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6636"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"math-review-of-roots-of-numbers","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-roots-of-numbers\/","title":{"rendered":"Math Review of Roots of Numbers"},"content":{"rendered":"

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

The root of any number is specified by the radical symbol (\u221a).\u00a0 It is the inverse operation to raising a number by an exponent.\u00a0 Roots may be rational numbers or irrational numbers.<\/p>\n

What Is the Square Root?<\/strong><\/p>\n

The square of any number is the number multiplied by itself.\u00a0 For example, 62<\/sup> equals 36.\u00a0 The inverse of that operation is taking the square root, specified with the radical symbol without a number above it.\u00a0 If 36 equals 62<\/sup>, then \u221a36 equals 6.\u00a0 Similarly, the square root of 16 is 4, because 4 times 4 equals 16.<\/p>\n

What Is the Principal Root?<\/strong><\/p>\n

However, there are 2 square roots for 36, both 6 and -6, because 62<\/sup> is equal to 36, and (-6)2<\/sup> is also equal to 36.\u00a0 However, the positive root of a number is referred to as the principal square root of the number. When both the positive and negative roots of a number are desired, the \u00b1 is used before the radical sign, and when just the negative square root is desired the symbol -\u221a is used.<\/p>\n

What About Negative Numbers?<\/strong><\/p>\n

The square root of a negative number is not a real number.\u00a0 There is no real number that multiplied by itself that will equal a negative number.\u00a0 For example, \u221a-25 does not equal -5, because -5 times -5 is not -25, but 25.\u00a0 Algebraically speaking, for any real number \u221aa2<\/sup> to equal a, a must not be negative.\u00a0 It can be 0, because the square root of 02<\/sup> or 0 times 0 is 0.\u00a0 Therefore, the square root of x4 <\/sup>\u00a0is x2<\/sup> as long as x is positive or zero, in order for the solution to be real.<\/p>\n

What About Rational and Irrational Numbers?<\/strong><\/p>\n

Many numbers are perfect squares and have rational square roots.\u00a0 For example, the square root of 16 is exactly 4 because 4 times itself is 16.\u00a0 The square root of 25 is exactly 5, because 5 times 5 is 25.\u00a0 What about the square root of 20?\u00a0 It will be somewhere between 4 and 5, but can only be approximated, as an irrational number.\u00a0 If the sides of a right triangle can be expressed in the Pythagorean theorem by a2<\/sup> + b2<\/sup> =c2<\/sup>, then the length of any side can either be a rational or an irrational number.\u00a0 For example, suppose one side measures 6 and one side measures 4.\u00a0 Then c2<\/sup> will equal 62 <\/sup>\u00a0+42<\/sup>, or 36 +16 =52.\u00a0 Side c will measure \u221a52, which is an irrational number between 7 and 8.<\/p>\n

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Overview The root of any number is specified by the radical symbol (\u221a).\u00a0 It is the inverse operation to raising a number by an exponent.\u00a0 Roots may be rational numbers or irrational numbers. What Is the Square Root? The square of any number is the number multiplied by itself.\u00a0 For example, 62 equals 36.\u00a0 The […]<\/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":[985,1476,1485,1498,1716],"class_list":["post-6636","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-irrational-numbers","tag-radical","tag-rational-numbers","tag-real-numbers","tag-square-roots"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6636","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=6636"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6636\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6636"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6636"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}