i would pick a number. since x<0, say x=-2

(-x*|x|)^1/2= [-(-2)*|-2|]^1/2
=> (2*2)^1/2
=2 (a square root is always +ive or 0. (non-negative)

so the expression translates to -x

=2 (a square root is always +ive or 0. (non-negative)

The number inside the square root has to be always positive,however the result that is, the answer obtained by taking square root can be positive or negative

You need to brush up your skills again scoobydbooby

for the gmat the number inside the square root has to be positive as otherwise we would be dealing with complex numbers which are not tested on the gmat.

and &#8730;(x^2) is equal to |x|. so &#8730;(2^2) is always |2| or +2

gmat740,
that was outright rude. always choose your words with caution, you never know when you have to eat them.

Now, now, here's the exact reason:

For all real numbers x,
sqrt{x^2} = |x| = x , if x > 0
= -x, if x < 0

As x<0, so answer is -x.

gmat740, you shouldn't say things like that about other forum members.

As for this problem, I see that you have made a similar reasoning in this post:

https://www.beatthegmat.com/gmat-prep-1- ... tml#139267

I've given the same explanation as what scoobydooby has given here.

-BM-