it would help if you posted the question in its entirety
Nice link, ps_dahiya....something new:
Let me see if I understand it correctly -
(-x|x|)^1/2 is our expression, and x is negative.
From the answer choices, the others are clearly out apart from x and -x. If x is the root, then we get the expression as sqrt (-(x).x)^1/2, which is the square root of a negative number. By definition this is impossible.
If the root is -x, then we get the expression as sqrt(-(-x).x)^1/2 which is the sqrt of a +ve number.