x is negative, plug x = -x
sqrt[(-(-x) |-x|)]
=sqrt[(x*x)]
= sqrt[x^2]
= x
but its given that x is -ve
Therefore value = -x
Option A.

In other words, because you original number was negative and it becomes positive, it's -1*original number. Not a fan of this question but good to know they ask this type of thing. This is almost brainteaser-like.

Something still eludes me on this question.
Say x= -4. Multiplying -x by |x|, I get 16. Doesn't this have two square roots?

Good question. I never actually explicitly thought about that one before, so I Googled it. The answer is that, while there are 2 square roots as you've stated (+ and -), the √ notation supposedly designates the "principle square root", which is the *positive* answer.

https://www.mathsisfun.com/algebra/square-root.html

That being said, this looks like a candidate question to be thrown out due to ambiguity. They really should not have offered option 4 to be absolutely clear.

tomada wrote:Something still eludes me on this question.
Say x= -4. Multiplying -x by |x|, I get 16. Doesn't this have two square roots?

haidgmat wrote:If x<0, then sq.rt.(-x|x|) is
1. -x
2. -1
3. 1
4. X
5. Sq.rt(x)

[spoiler]OA:A[/spoiler]

Now ,x<0.
So, |x|=-x.
Hence,the ques. becomes sqrt[(-x)*(-x)]
=sqrt[x^2]
=|x|
Now since x<0,|x| would be -x which is A.

Alternate Solution:-Pick any -ve number(say -2) and put in the question.

Trick:-A person can confuse between option (1) and (4).Do keep in mind that you are dealing with a -ve number hence "X" can never be the answer.