From GMATPrep

[chatekar]

If x < 0 then sqrt(-x|x|) is

1. –x
2. -1
3. 1
4. x
5. sqrt(x)

My answer was x, but the GMATprep says its -x

Thanks

[jayhawk2001]

The sqrt of a number cannot be negative. We are given x < 0 and so
answer has to be -x (which is a positive number).

[beny]

Are you sure this is a GMATPrep question...? GMAT does not use imaginary numbers.

[jayhawk2001]

Are you sure this is a GMATPrep question...? GMAT does not use imaginary numbers.

Can you please clarify on what the imaginary number is in this case.

-x|x| is positive when x<0. So, we are not trying to take the
square-root of a negative number to get an imaginary number.

[givemeanid]

The sqrt of a number cannot be negative.

Every positive number has TWO square roots. One positive, one negative.

36 = 6*6 = -6 * -6
sqrt(36) = 6 or -6

[jayhawk2001]

Every positive number has TWO square roots. One positive, one negative.

36 = 6*6 = -6 * -6
sqrt(36) = 6 or -6

Actually let me make a small distinction --

If x^2 = 36, you can say x = +6 or x = -6

If you are asked to find sqrt(36), there is only 1 root and that is +6.

I learnt this important concept through this forum. Please check https://www.beatthegmat.com/viewtopic.php?t=2183

[chatekar]

jayhawk2001,

I'm totally confused. First of all I haven't clearly understood the explanation for my question.
And the other thing, I don't understand why sqrt(36) is always 6?

Thanks
Suhas

[givemeanid]

Actually let me make a small distinction --

If x^2 = 36, you can say x = +6 or x = -6

If you are asked to find sqrt(36), there is only 1 root and that is +6.

I learnt this important concept through this forum. Please check https://www.beatthegmat.com/viewtopic.php?t=2183

From the thread you linked to: "Every positive number n has two square roots, one positive and the other negative, but root-n denotes the positive number whose square is n".

Son of a *#$@%. Completely missed that. Thanks buddy.