{"id":1635,"date":"2012-05-16T11:28:48","date_gmt":"2012-05-16T11:28:48","guid":{"rendered":"http:\/\/www.schooltutoring.com\/scholarship\/?p=1635"},"modified":"2014-12-02T08:33:45","modified_gmt":"2014-12-02T08:33:45","slug":"operations-on-radicals","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/05\/16\/operations-on-radicals\/","title":{"rendered":"Operations on Radicals"},"content":{"rendered":"<p>A radical may be defined as a positive irrational number of the type <a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/surd.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1636\" title=\"surd\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/surd.png\" alt=\"\" width=\"27\" height=\"27\" \/><\/a>, where the symbol\u00a0<a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/surd-symbol.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1637\" title=\"surd symbol\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/surd-symbol.png\" alt=\"\" width=\"27\" height=\"25\" \/><\/a> is called the radical sign, the index n is called the order of the radical and x the radicand. A number <a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/surd.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1636\" title=\"surd\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/surd.png\" alt=\"\" width=\"27\" height=\"27\" \/><\/a>can be a radical if and only if it is an irrational number and the radicand is a positive rational number. When the order is not mentioned it is taken as 2.<\/p>\n<p>If two radicals have the same order and the same radicands in their reduced form they are called <strong>like radicals. <\/strong><\/p>\n<p><strong>Addition and subtraction of radicals<\/strong><\/p>\n<p>Only like radicals can be added or subtracted by adding or subtracting their coefficients.<\/p>\n<p>Example 1:<\/p>\n<p><a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/op-on-surds-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1638\" title=\"op on surds 1\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/op-on-surds-1.png\" alt=\"\" width=\"129\" height=\"38\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Example 2:<\/p>\n<p><a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/op-on-surds-2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1639\" title=\"op on surds 2\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/op-on-surds-2.png\" alt=\"\" width=\"143\" height=\"89\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Multiplication of radicals<\/strong><\/p>\n<p>Radicals of different orders are first converted to same order by finding the LCM of orders of the given radicals and then multiplied using the rule <a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/surd-law.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1640\" title=\"surd law\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/surd-law.png\" alt=\"\" width=\"130\" height=\"29\" \/><\/a><\/p>\n<p><a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/mul-of-surds1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1679\" title=\"mul of surds\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/05\/mul-of-surds1.png\" alt=\"\" width=\"379\" height=\"432\" srcset=\"https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2012\/05\/mul-of-surds1.png 379w, https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2012\/05\/mul-of-surds1-263x300.png 263w\" sizes=\"auto, (max-width: 379px) 100vw, 379px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>SchoolTutoring Academy 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 Kitchener visit: <a href=\"https:\/\/schooltutoring.com\/private-tutoring-in-kitchener-ontario\">Tutoring in Kitchener.<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A radical may be defined as a positive irrational number of the type , where the symbol\u00a0 is called the radical sign, the index n is called the order of the radical and x the radicand. A number can be a radical if and only if it is an irrational number and the radicand is [&hellip;]<\/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":[49,57,1163,1168,1252,1761,1769],"class_list":["post-1635","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-addingradicals","tag-additionofradicals","tag-multiplicationofradicals","tag-multiplyingradicals","tag-operationsonradicals","tag-subtractingradicals","tag-subtractionofradicals"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/1635","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=1635"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/1635\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=1635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=1635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=1635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}