Please refer to the attached image.

The answer is -x.

a) how is the answer to a sqrt negative?

b) isn't the sqrt of (-x) * (-x) = sqrt of x^2 = x.

What am I missing?

Thank you.

Really confusing. The question begins by telling us that x is negative. The second term, [x] (those are supposed to be absolute value signs) actually becomes -x. Think about it - absolute value means the number becomes positive. x by itself indicates a negative number. So to indicate the positive version of the negative number, I have to put another negative sign in front of it, to cancel out the negatives.

That leaves me with SQRT(-x*-x). The square root of that is -x, which is not actually a negative number - it's a positive number. (Remember, again, that x is negative.)

those tricksters!!

Another tip : Square root of a negative number will have an 'i' (imaginary number) in its answer

eg. square root of -16 = 4i.

Hence if the answer choices have a -ve number without an 'i' they can be straight away ruled out. Additionally I dont think GMAT test imaginary numbers.

Hence if you get a negative number under the square root sign check to see if the answer choices have an 'i' or you have made a mistake.

Given X is negative.

So (-X) is positive.
|X| is always positive.

So (-X) multiplied by |X| is also positive which is also equal to Square of X. Its square root can be -X or +X

Since they have given the Radical sign and there is no negative sign before the radical sign the resultant expression should be Positive. For that it has to be (-X) (Because X is negative from the first statement).

Hope it helps

"have a -ve number"

Don't understand the lingo, what does "ve" or "-ve" stand for?

thanks.

-ve : negative number
ve : positive number

The GMAT doesn't test imaginary numbers. You'll never see an i indicating an imaginary number on the test.