BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

can we consider SQRT(n) be negative?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 158
Joined: Mon Dec 03, 2007 8:32 am
Thanked: 7 times
by StarDust845 » Mon Dec 24, 2007 9:00 am
Hi,

There is a problem which depended on SQRT(n) where n is positive. I assumed that SQRT(n) could be negative also, but the answer was wrong.

Can't we assume SQRT(n) to be negative in DS?

Thanks,
Calista.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Quantitative Reasoning |
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member
Location: India
Thanked: 51 times

by gabriel » Mon Dec 24, 2007 10:14 am
sqrt of a number is always positive... the common notion that sqrt of a number like 4 is both 2 and -2 is wrong .. 2 and -2 are the roots of the equation x^2-4=0, whereas the sqrt of 4 is only 2 ..

Regards
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 158
Joined: Mon Dec 03, 2007 8:32 am
Thanked: 7 times

by StarDust845 » Mon Dec 24, 2007 8:04 pm
Are you talking about mathematics in general? Or are you talking about what I should consider for GMAT? because

https://en.wikipedia.org/wiki/Square_root

In the above link it says sqrt(9) could be -3 or 3.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member
Location: India
Thanked: 51 times

by gabriel » Mon Dec 24, 2007 8:36 pm
I guess I should have been a little more specific, the nonnegative sqrt of a number is called the principal sqrt of that number and unless specified, when we talk about a sqrt of a number we are talking about the principal sqrt, this is true for both general mathematics and GMAT.

Regards
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sat May 05, 2007 6:05 am
Thanked: 1 times

by srawat_itpro » Fri Dec 28, 2007 2:56 am
gabriel wrote:I guess I should have been a little more specific, the nonnegative sqrt of a number is called the principal sqrt of that number and unless specified, when we talk about a sqrt of a number we are talking about the principal sqrt, this is true for both general mathematics and GMAT.

Regards
Not necessarily so!! I have seen a few questions where it was not explicitly specified to consider -ve root also but still the answer was dependent on it. I guess unless explicitly mentioned such as X^2 > 0 or X^2 is positive , one should consider both +ve and -ve roots. Generally in questions which require one to determine factors of X^2 , we should consider only +ve factors.

Rgds
Sandeep
Decide and do it !!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member
Location: India
Thanked: 51 times

by gabriel » Fri Dec 28, 2007 5:13 am
srawat_itpro wrote:
gabriel wrote:I guess I should have been a little more specific, the nonnegative sqrt of a number is called the principal sqrt of that number and unless specified, when we talk about a sqrt of a number we are talking about the principal sqrt, this is true for both general mathematics and GMAT.

Regards
Not necessarily so!! I have seen a few questions where it was not explicitly specified to consider -ve root also but still the answer was dependent on it. I guess unless explicitly mentioned such as X^2 > 0 or X^2 is positive , one should consider both +ve and -ve roots. Generally in questions which require one to determine factors of X^2 , we should consider only +ve factors.

Rgds
Sandeep
I think the question you are talking about are questions based on inequality, in which case both the roots have to be considered. If the question is based on a simple equation and we are asked the root of a positive number then we do consider the positive root unless specified, there are reasons for it (Hint : Pythagoras theorem) which is beyond the scope of this question.

I am absolutely sure that this is also mentioned in OG 11, but I dont have mine any more, if any one knows about the question in the explanation of which this property is mentioned then please do post the question number over here.

Regards
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 423
Joined: Thu Dec 27, 2007 1:29 amFollowed by: 2 members
Location: Hyderabad, India
Thanked: 36 times
GMAT Score:770

by simplyjat » Tue Jan 08, 2008 10:27 pm
Square root of a number is always positive and negative. i.e. sqrt(9) = +3 & -3. And GMAT specifically checks that you consider both the alternatives. The equation "X^2 -9 = 0", can be simplified to X^2 = 9 and X = sqrt(9); giving the answer X = +3 or -3.

Now there are situations (exceptions), such as length, where the negative number does not make any sense. And in these cases the negative value can be discarded. i.e. if the area of a square is 9, then after calculations, we can omit -3 as length is never negative.
simplyjat
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 158
Joined: Mon Dec 03, 2007 8:32 am
Thanked: 7 times

by StarDust845 » Wed Jan 09, 2008 11:36 am
simplyjat wrote:Square root of a number is always positive and negative. i.e. sqrt(9) = +3 & -3. And GMAT specifically checks that you consider both the alternatives. The equation "X^2 -9 = 0", can be simplified to X^2 = 9 and X = sqrt(9); giving the answer X = +3 or -3.

Now there are situations (exceptions), such as length, where the negative number does not make any sense. And in these cases the negative value can be discarded. i.e. if the area of a square is 9, then after calculations, we can omit -3 as length is never negative.
You are right, but what gabriel was trying to get at is this:

If n is a positive integer 4, what is the sqrt(n)? We consider only +2.

But for your question for something like x^2 - 4 = 0. What is X? It can be +2 or -2. There is a subtle difference.

(As gabriel wrote earlier, in math review in OG11, they gave an example).

Calista.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 41
Joined: Wed Jan 02, 2008 9:21 pm
Location: New York, NY
Thanked: 9 times

by solaris » Wed Jan 09, 2008 11:39 am
If a question on the GMAT refers specifically to a number which is sqrt(x), it is ALWAYS referring to the positive root of 'x'.

Obviously, if it talks about x^2 then you have to assume both +ve and -ve values of x.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Aug 18, 2017 1:25 pm
AFAIK this is a convention dating back to the ancient Greeks, who didn't use/believe in/consider negative numbers, but did make great use of square roots. √16 = 4, always and forever, because we used the √ symbol.

On the other hand, x * x = 16 has two roots, x = 4 and x = -4.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1