{"id":4746,"date":"2012-11-02T15:55:04","date_gmt":"2012-11-02T15:55:04","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=4746"},"modified":"2014-12-02T08:31:57","modified_gmt":"2014-12-02T08:31:57","slug":"algebra-square-roots","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/11\/02\/algebra-square-roots\/","title":{"rendered":"Algebra: Square Roots"},"content":{"rendered":"

Square root of a positive real number:<\/strong><\/p>\n

The square root of a real number x<\/em><\/strong> is s<\/em><\/strong> which satisfies the equation x = s2<\/sup>.<\/em><\/strong> If x = s2<\/sup> then x = (-s)2<\/sup> is also satisfied because (-s)2<\/sup> = s2<\/sup>. So, the square root of x is \u00b1s<\/em><\/strong> and it is read as plus or minus s<\/em><\/strong>. \u00a0Square root of x is symbolically denoted by \u221ax. Thus the square root is mathematically defined as follows.<\/p>\n

\u221ax = \u00b1 s \u2194 x = s2<\/sup><\/p>\n

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

1)\u00a0\u00a0\u00a0\u00a0\u00a0 \u221a9 =\u221a32<\/sup> = \u00a0\u00b13<\/p>\n

2)\u00a0\u00a0\u00a0\u00a0\u00a0 \u221a25 = \u221a52<\/sup> = \u00b15<\/p>\n

So, every square root gives two values, one with positive sign and with negative sign. Here, the positive value is called the principal square root. In general, the square root of a number is taken as its principal square root.<\/p>\n

There is a reason for talking about the principal square root of a number. If we take the function f(x)=x2<\/sup> then its inverse function g(x)=\u00b1 \u221ax. Thus every value of x<\/em><\/strong> is mapped onto two values. Then g(x) cannot be a function.\u00a0 Thus, if we define the square root of x<\/em><\/strong> to be the principal square root then g(x) becomes a function. This is the reason why the principal square root is defined.<\/p>\n

Square root of a negative number:<\/strong><\/p>\n

Let x be a negative real number and s be its square root. Then by the definition of square root<\/p>\n

x = s2<\/sup> and x = (-s)2<\/sup>= (is)2<\/sup> (because i2<\/sup>=-1)<\/p>\n

So \u221ax = \u00b1is.<\/p>\n

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

1)\u00a0\u00a0\u00a0\u00a0\u00a0 \u221a-9 =\u221a(i3)2<\/sup> = \u00a0\u00b13i<\/p>\n

2)\u00a0\u00a0\u00a0\u00a0\u00a0 \u221a25 = \u221a(i5)2<\/sup> = \u00b15i<\/p>\n

Do you also need help with Standardized Tests? Take a look at our Test Prep tutoring services.<\/a> <\/p>\n

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 Yonkers visit: Tutoring in Yonkers. <\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Square root of a positive real number: The square root of a real number x is s which satisfies the equation x = s2. If x = s2 then x = (-s)2 is also satisfied because (-s)2 = s2. So, the square root of x is \u00b1s and it is read as plus or minus […]<\/p>\n","protected":false},"author":19,"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":[704,969,1184,1363,1715],"class_list":["post-4746","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-function","tag-inverse","tag-negative","tag-positive","tag-square-root"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/4746","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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=4746"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/4746\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=4746"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=4746"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=4746"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}