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.
can we consider SQRT(n) be negative?
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 158
- Joined: Mon Dec 03, 2007 8:32 am
- Thanked: 7 times
- gabriel
- Legendary Member
- Posts: 986
- Joined: Wed Dec 20, 2006 11:07 am
- Location: India
- Thanked: 51 times
- Followed by:1 members
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
Regards
-
- Master | Next Rank: 500 Posts
- Posts: 158
- Joined: Mon Dec 03, 2007 8:32 am
- Thanked: 7 times
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.
https://en.wikipedia.org/wiki/Square_root
In the above link it says sqrt(9) could be -3 or 3.
- gabriel
- Legendary Member
- Posts: 986
- Joined: Wed Dec 20, 2006 11:07 am
- Location: India
- Thanked: 51 times
- Followed by:1 members
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
Regards
-
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Sat May 05, 2007 6:05 am
- Thanked: 1 times
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.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
Rgds
Sandeep
Decide and do it !!!
- gabriel
- Legendary Member
- Posts: 986
- Joined: Wed Dec 20, 2006 11:07 am
- Location: India
- Thanked: 51 times
- Followed by:1 members
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.srawat_itpro wrote: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.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
Rgds
Sandeep
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
- simplyjat
- Master | Next Rank: 500 Posts
- Posts: 423
- Joined: Thu Dec 27, 2007 1:29 am
- Location: Hyderabad, India
- Thanked: 36 times
- Followed by:2 members
- GMAT Score:770
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.
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
-
- Master | Next Rank: 500 Posts
- Posts: 158
- Joined: Mon Dec 03, 2007 8:32 am
- Thanked: 7 times
You are right, but what gabriel was trying to get at is this: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.
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.
-
- Senior | Next Rank: 100 Posts
- Posts: 41
- Joined: Wed Jan 02, 2008 9:21 pm
- Location: New York, NY
- Thanked: 9 times
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.
Obviously, if it talks about x^2 then you have to assume both +ve and -ve values of x.
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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.
On the other hand, x * x = 16 has two roots, x = 4 and x = -4.