![\"Manhattan](\"http:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2017\/04\/4-27-17-social-2.png\")
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Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We\u2019re not kidding! <\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n <\/i><\/b>Here\u2019s one of the most common math questions my students ask: \u201cWhat\u2019s up with negative numbers and square roots on the GMAT?\u201d Luckily, the answer doesn\u2019t involve a lot of complex rules. In this quick article, I\u2019ll lay out the issues surrounding square roots and negative numbers, and share everything you need to know to handle them confidently. <\/span><\/p>\n If you\u2019ve been studying for a while, or if you\u2019ve worked your way through <\/span>Foundations of Math<\/span><\/a>, you probably know that there\u2019s a strange interaction between negative numbers and exponents. If you square a negative number, the result is positive. If you square a positive number, the result is also positive. Squaring a number makes the negative sign \u2018go away.\u2019 This is where the problem with square roots comes in.<\/span><\/p>\n Suppose you\u2019re looking at an equation that looks like this:<\/span><\/p>\n x\u00b2<\/span><\/i>\u00a0<\/span>= 4<\/span><\/p>\n You want to find the value of <\/span>x<\/span><\/i>. Before you start writing out square root signs, think for a moment about what this equation actually means. \u201cWhen you square some number, the result is positive 4. What is that number?\u201d Well, the number could be positive 2. It could also be negative 2. There\u2019s no way to know which. You have to give two answers: one positive answer, and one negative answer. \u00a0<\/span><\/p>\n On the other hand, suppose you\u2019ve got an equation that looks like this: <\/span><\/p>\n x<\/em>=\u221a<\/span>4<\/span><\/p>\n Wait. Isn\u2019t that just the same equation? Not quite. When the GMAT gives you a <\/span>square root symbol<\/b>, it\u2019s referring to <\/span>one specific value<\/b>: the positive square root. In other words, on the GMAT, the square root of 4 is 2. If the GMAT gives you this equation, you only have to give <\/span>one<\/span><\/i> answer: the positive one. <\/span><\/p>\n That\u2019s pretty weird, and it might not be what you learned in your middle school math class. But it <\/span>is<\/span><\/i> how square roots on the GMAT work. Here\u2019s what you need to memorize:<\/span><\/p>\n If I see <\/b>\u201c<\/span>x\u00b2<\/span><\/i>\u00a0<\/span>= something,\u201d <\/span>I think<\/b> \u201cx could be positive or negative.\u201d<\/span><\/p>\n If I see<\/b> the square root of a value, <\/span>I think<\/b> \u201cthe answer will always be positive.\u201d<\/span><\/p>\n Try using those ideas to answer this Data Sufficiency question. The answer is at the end of this article. <\/span><\/p>\n If y = 2<\/span>4<\/span>, what is the value of <\/span>x<\/span><\/i>?<\/span><\/p>\n (1)<\/span> x\u00b2<\/span><\/i>\u00a0<\/span>= <\/span>y In tougher problems, you might also see variables under a square root. Because there\u2019s a square root, you need to make sure you get the <\/span>positive<\/span><\/i> answer! You\u2019ll do that by using <\/span>absolute values<\/b>. Here\u2019s an example:<\/span><\/p>\n If <\/span>x<\/span><\/i> < 0, which of the following must equal -1? <\/span><\/p>\n All three of the answer choices contain the expression \u221ax\u00b2<\/em><\/span>. How does this simplify? Well, it has to simplify to a positive number, because of the rules established above. It can\u2019t just simplify to <\/span>x<\/span><\/i>, because the question states that <\/span>x<\/span><\/i> is negative! To make it positive, take the absolute value: \u221a<\/span>x\u00b2<\/span><\/em>=|x<\/em>|<\/span>. From here, simplify the expressions in order to find that (A) equals -1, while (B) and (C) both equal 1. The correct answer is (A). <\/span><\/p>\n Finally, how about that Data Sufficiency question from earlier? The right answer to that one is (B). The first statement is insufficient, because there are still two possible values for <\/span>x<\/span><\/i>. <\/span>x<\/span><\/i> could equal 4, or it could equal -4. However, the second statement includes a square root, which tells you that the answer is definitely positive. In this case, <\/span>x<\/span><\/i> has to be positive 4. Since there\u2019s a single correct answer to the question, the second statement is sufficient. <\/span><\/p>\n From now on, don\u2019t assume that <\/span>x\u00b2\u00a0<\/span><\/i>= 4 and <\/span>x\u00a0<\/em>=\u00a0\u221a<\/span>4<\/span> mean exactly the same thing! On the GMAT, they\u2019re close, but not a perfect match. Pay close attention to which type of equation the GMAT gives you, so you know how many solutions there should be. ?<\/span><\/p>\n Want more guidance from our GMAT gurus? You can attend the first session of any of our online or in-person GMAT courses absolutely free! We\u2019re not kidding. <\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n Chelsey Cooley<\/a> Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We\u2019re not kidding! Check out our upcoming courses here. Here\u2019s one of the most common math questions my students ask: \u201cWhat\u2019s up with negative numbers and square roots on the GMAT?\u201d Luckily, the answer […]<\/p>\n","protected":false},"author":127,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[873,929,52871,930,2,8],"tags":[53025],"yst_prominent_words":[],"class_list":["post-13605","post","type-post","status-publish","format-standard","hentry","category-for-current-studiers","category-gmat-prep","category-gmat-strategies","category-gmat-study-guide","category-how-to-study","category-quant-on-gmat","tag-square-roots-on-the-gmat"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/13605","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/users\/127"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=13605"}],"version-history":[{"count":3,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/13605\/revisions"}],"predecessor-version":[{"id":13698,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/13605\/revisions\/13698"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=13605"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=13605"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=13605"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=13605"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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\n<\/span><\/i>(2) x\u00a0<\/em>=\u00a0\u221a<\/span>y<\/span><\/em><\/p>\n![\"Manhattan](\"http:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2017\/04\/cc-43.png\")
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\n![\"Chelsey](\"https:\/\/cdn2.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2015\/11\/chelsey-cooley-150x150.jpg\" "\\"Chelsey")
<\/a> is a Manhattan Prep instructor based in Seattle, Washington.<\/strong>\u00a0<\/em><\/i><\/b>Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master\u2019s degree in linguistics, a 790 on the GMAT, and a perfect 170\/170 on the GRE.\u00a0<\/em><\/i>Check out Chelsey\u2019s upcoming GRE prep offerings here<\/a>.<\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"