{"id":7771,"date":"2016-09-06t13:34:19","date_gmt":"2016-09-06t20:34:19","guid":{"rendered":"\/\/www.catharsisit.com\/hs\/?p=7771"},"modified":"2016-09-06t13:34:39","modified_gmt":"2016-09-06t20:34:39","slug":"mental-math-shortcut-n2-1-sat-video-post","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/sat\/mental-math-shortcut-n2-1-sat-video-post\/","title":{"rendered":"mental math shortcut: perfect squares \u2013 1 | sat video post"},"content":{"rendered":"

https:\/\/youtu.be\/9hulsctjbks<\/a><\/p>\n

a handy sat math shortcut \u2013 n2<\/sup> \u2013 1<\/h2>\n

many of us have a pretty good sense of what the squares of the first 15 integers are. sure, you might be a bit shaky on \u201813\u2019 and \u201814\u2019 but you should be comfortable with the rest. just to be sure, i\u2019ll reproduce those below:<\/p>\n

1^2 = 1
\n2^2 = 4
\n3^2 = 9
\n4^2 = 16
\n5^2 = 25
\n6^2 = 36
\n7^2 = 49
\n8^2 = 64
\n9^2 = 81
\n10^2 = 100<\/p>\n

11^2 = 121
\n12^2 = 144
\n13^2 = 169
\n14^2 = 196
\n15^2 = 225<\/p>\n

here are more squares students tend to know:
\n16^2 = 256
\n20^2 = 400
\n25^2 = 625
\n30^2 = 900<\/p>\n

(if you know all these, that\u2019s pretty solid! you don\u2019t have to memorize anymore.)<\/p>\n

why did i even bring this up in the first place? well, i have a cool mental math shortcut.<\/strong> assuming you know the above, you also know the following:<\/p>\n

11 x 13, 14 x 16, 15×17 and even the crazy 29×31.<\/p>\n

how is that possible?<\/p>\n

well, what if i told you that n^2 \u2013 1 = (n \u2013 1)(n + 1)<\/p>\n

big deal, you say. you already know basic algebra? and what does this have to do with squares?<\/p>\n

well, let\u2019s say n = 20.<\/p>\n

see, by knowing that 20^2 = 400, then the product of one integer less than 20\u2014the number 19\u2014and one integer greater than 20\u2014the number 21\u2014will be 400-1, which equals 399.<\/p>\n

try it with any of the numbers above. for instance, we know that 12^2 = 144. therefore, 11 x 13 = 143.<\/p>\n

29 x 31?<\/p>\n

well, what\u2019s 30^2 \u2013 1.<\/p>\n

just like that, voila! you\u2019ve doubled your knowledge of squares above.<\/p>\n","protected":false},"excerpt":{"rendered":"

a handy sat math shortcut \u2013 n2 \u2013 1 many of us have a pretty good sense of what the squares of the first 15 integers are. sure, you might be a bit shaky on \u201813\u2019 and \u201814\u2019 but you should be comfortable with the rest. just to be sure, i\u2019ll reproduce those below: 1^2 […]<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[],"ppma_author":[24882],"acf":[],"yoast_head":"\nmental math shortcut: perfect squares \u2013 1 | sat video post - magoosh blog | high school<\/title>\n<meta name=\"description\" content=\"check out our sat math video to learn how to find the product of larger numbers in your head simply by knowing the mental math shortcut to perfect squares.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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lele","image":{"@type":"imageobject","inlanguage":"en-us","@id":"\/\/www.catharsisit.com\/hs\/#\/schema\/person\/image\/9f063fdc4c0268d1eac74c41e0906a03","url":"https:\/\/secure.gravatar.com\/avatar\/198545d5a4baea0ba0fd0c0fc8a5d466?s=96&d=mm&r=g","contenturl":"https:\/\/secure.gravatar.com\/avatar\/198545d5a4baea0ba0fd0c0fc8a5d466?s=96&d=mm&r=g","caption":"chris lele"},"description":"chris graduated from ucla with a ba in psychology and has 20 years of experience in the test prep industry. he's been quoted as a subject expert in many publications, including us news, gmac, and business because.","sameas":["https:\/\/www.facebook.com\/chrislelemagoosh1\/","ttps:\/\/www.linkedin.com\/in\/chris-lele-095005a0","https:\/\/twitter.com\/chrismagoosh","https:\/\/www.youtube.com\/channel\/ucz4sgyj6l0cgnvnihy8gy6w"],"knowsabout":["gre","gmat","sat","act","mcat (cars)","lsat"],"jobtitle":"principal curriculum manager","worksfor":"magoosh","url":"\/\/www.catharsisit.com\/hs\/author\/chris\/"}]}},"authors":[{"term_id":24882,"user_id":10,"is_guest":0,"slug":"chris","display_name":"chris lele","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/198545d5a4baea0ba0fd0c0fc8a5d466?s=96&d=mm&r=g","user_url":"","last_name":"lele","first_name":"chris","description":"chris lele is the principal curriculum manager (and <a href=\"https:\/\/www.amazon.com\/vocabulary-builder-workbook-activities-must-know\/dp\/193975481x\" rel=\"noopener noreferrer\">vocabulary wizard<\/a>) at magoosh. chris graduated from ucla with a ba in psychology and has 20 years of experience in the test prep industry. he's been quoted as a subject expert in many publications, including<a href=\"https:\/\/www.usnews.com\/education\/best-colleges\/slideshows\/10-test-prep-tips-for-sat-and-act-takers\" rel=\"noopener noreferrer\"> us news<\/a>,<a href=\"https:\/\/www.mba.com\/exams-and-exam-prep\/gmat-exam\/why-take-the-gmat-in-2021-when-many-schools-are-test-optional\" rel=\"noopener noreferrer\"> gmac<\/a>, and<a href=\"https:\/\/www.businessbecause.com\/news\/gmat\/3263\/mba-admissions-gre-challenges-gmat\" rel=\"noopener noreferrer\"> business because<\/a>.\r\n\r\n\r\nin his time at magoosh, chris has taught countless students how to tackle the<a href=\"https:\/\/www.amazon.com\/gre-prep-magoosh\/dp\/1939418917\/\" rel=\"noopener noreferrer\"> gre<\/a>, gmat, sat, act, mcat (cars), and lsat exams with confidence. some of his students have even gone on to get near-perfect scores. you can find chris on <a href=\"https:\/\/www.youtube.com\/channel\/ucz4sgyj6l0cgnvnihy8gy6w\">youtube<\/a>,<a href=\"https:\/\/www.linkedin.com\/in\/chris-lele-095005a0\"> linkedin<\/a>, <a href=\"https:\/\/twitter.com\/chrismagoosh\">twitter<\/a> and <a href=\"https:\/\/www.facebook.com\/chrislelemagoosh1\/\">facebook<\/a>!"}],"_links":{"self":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts\/7771"}],"collection":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/comments?post=7771"}],"version-history":[{"count":0,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts\/7771\/revisions"}],"wp:attachment":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/media?parent=7771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/categories?post=7771"},{"taxonomy":"post_tag","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/tags?post=7771"},{"taxonomy":"author","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/ppma_author?post=7771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}