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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## squares versus square roots tagged by: Brent@GMATPrepNow ##### This topic has 2 expert replies and 2 member replies ## squares versus square roots I know it's a rule that when x^2 = 81, the solution is x = 9 or -9, and when x = sqrt(81), the answer is just positive 9. So, I just take this as a given on the GMAT. But I'm still wondering... why is this true?? It doesn't seem to make sense. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 This all has to do with agreed-upon notation. From the Official Guide: A square root of a number n is a number that, when squared, is equal to n. Every positive number n has two square roots, one positive and the other negative, but âˆšn denotes the positive number whose square is n. For example, âˆš9 denotes 3. Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! Master | Next Rank: 500 Posts Joined 23 Jan 2009 Posted: 131 messages Followed by: 15 members Upvotes: 59 It is an agreed upon convention, which means âˆš81=9. If we have x^2=81, then we write x = +âˆš81= 9 or x= -âˆš81= -9. Cheers, Dabral _________________ Free Video Explanations: 2018 OFFICIAL GUIDE FOR GMAT REVIEW. Junior | Next Rank: 30 Posts Joined 30 May 2014 Posted: 20 messages Upvotes: 1 It usually depends on what is being asked in the question. For example if the question asks you to find weight or distance or something that you know can certainly not be negative then you just neglect the negative root of that quadratic equation. Otherwise, there always exist 2 roots of a quadratic equation and if the question is typically about finding the roots then just giving the positive root will suffice. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Hi All, There's actually a rather simple way to deal with this issue. Focus on what the prompt GIVES YOU to work with. If you're given a square root sign, then you are responsible for the POSITIVE answer ONLY. If you're given a squared term (e.g. X^2 = 25), then you are responsible for BOTH the POSITIVE and NEGATIVE answers. By extension, if you're given a quadratic (e.g. X^2 +2X - 3), then you're responsible for BOTH answers (regardless of whether they're positive or negative). In questions involving logical restrictions (geometry, etc.), there's no such thing as a "negative side length", which is why the Pythagorean Theorem is concerned with just the positive results. GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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