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Square Root Question

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Square Root Question

by jaybrium » Thu Sep 18, 2008 9:22 am
Beat the GMAT Community,

I've read that the GMAT always assumes that a number in the square root symbol is the positive square root. Is this true?

Take this DS example:

** I'm using "v" as the square root symbol **

What is the value of X?

1) X = v9

2) X^2 = 9

If what I stated above is true, then the answer would be A. My line of thinking is that both result in x = -3 and x = 3 so the answer would be E.

If someone could clearify this, it would be greatly appreciated. I don't want to lose points over something like this...

Thanks,

- Jay
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Re: Square Root Question

by Ian Stewart » Thu Sep 18, 2008 10:20 am
jaybrium wrote:Beat the GMAT Community,

I've read that the GMAT always assumes that a number in the square root symbol is the positive square root. Is this true?
Technically, the 'square root' or 'radical' symbol means the 'non-negative square root' (because it can be equal to zero). But yes, what you say above is correct, and the answer to your DS question should be A. While it's true that 9 has two square roots, 3 and -3, if you see the square root symbol over the number 9, that is equal to 3, and only 3.
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by jaybrium » Thu Sep 18, 2008 11:36 am
Thanks for clearing that up for me Ian. One thing though- what do you mean when you say "because it can be equal to zero." What can be equal to zero?

Thanks again.

- Jay
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by Ian Stewart » Thu Sep 18, 2008 11:45 am
jaybrium wrote:Thanks for clearing that up for me Ian. One thing though- what do you mean when you say "because it can be equal to zero." What can be equal to zero?
Square roots can be equal to zero. If you see, say, sqrt(x), where I'm using 'sqrt' to mean the square root symbol, then it is not technically correct to conclude that sqrt(x) is positive. It might be that x is equal to zero, and thus that sqrt(x) also equals zero. You can, of course, be completely sure that sqrt(x) is not negative, however. A minor technicality, but potentially important on the occasional question.
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by jaybrium » Thu Sep 18, 2008 12:11 pm
Makes sense. Thanks for clearing that up for me.
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by astrouse » Fri Dec 19, 2008 2:40 pm
I understand what you are saying, but this confuses me with the current question I am working on:

x does note equal 0
x^(1/2)
a) negative
b) positive
c) uncertain

I would say that it is uncertain because the square root sign is not here...however, in the answer to this question they say..."this is equivalent to square root of x and all square roots are (except for 0) positive values.

But...b/c the square root is not in the question, I cannot assume it is positive, right?
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by EmilKhalikov » Fri Dec 19, 2008 8:58 pm
From California Mathematical Project:
"square root - The square roots of n are all the complex numbers m so that m^2 = n. The square roots of 16 are 4 and -4. The square roots of -16 are 4 i and -4 i"

So technically if you ask a mathematician what is square root of 4, he/she would say -2 and 2, but if we go outside of "math" world, everyone treat square root like a positive number.

P.S.: x^(1/2) could be either positive or i * positive...

P.P.S.: radicant of x is different story. Some math books use it as an arithmetic root only (positive answer), others use it as usual (positive&negative). And we are talking about upper devision math books here
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by Tomn » Sun Dec 21, 2008 1:03 pm
Since it is an exponent, you are going to get two answers... Graph it if you don't fully understand.
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by rajataga » Wed Dec 24, 2008 8:21 am
So what does GMAT say finally.....that is most important, not what other books say....

Can somebody else please also confirm what the others have said?

does radical(x) always considered by the GMAT to be positive? (assuming x is positive)

PLEASE PEOPLE WHO ARE SURE ABOUT THIS CONFIRM GMACs STANDPOINT ON THIS SPECIFICALLY. DONT REALLY CARE ABOUT OTHER BOOKS RIGHT NOW....
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