• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
This topic has expert replies
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: 12 Apr 2014

squares versus square roots

by gmatdestroyer1 » Sat May 03, 2014 3:56 pm
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.


User avatar
GMAT Instructor
Posts: 13519
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1256 members
GMAT Score:770

by Brent@GMATPrepNow » Sat May 03, 2014 4:42 pm
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 √n denotes the positive number whose square is n. For example, √9 denotes 3.

Brent Hanneson - Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide
Sign up for free Question of the Day emails
And check out all of these free resources

User avatar
Master | Next Rank: 500 Posts
Posts: 131
Joined: 23 Jan 2009
Location: California
Thanked: 59 times
Followed by:15 members

by dabral » Fri May 23, 2014 10:22 am
It is an agreed upon convention, which means √81=9. If we have x^2=81, then we write x = +√81= 9 or x= -√81= -9.

Free Video Explanations: 2018 OFFICIAL GUIDE FOR GMAT REVIEW.

Junior | Next Rank: 30 Posts
Posts: 20
Joined: 30 May 2014
Thanked: 1 times

by sukriti2hats » Sat May 31, 2014 3:56 am
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.


User avatar
Elite Legendary Member
Posts: 10333
Joined: 23 Jun 2013
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:498 members
GMAT Score:800

by Rich.C@EMPOWERgmat.com » Sat May 31, 2014 9:07 am
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,
Contact Rich at Rich.C@empowergmat.com