since X is negative
|x|=-x
sqrt(-x|x|)= sqrt(-x*-x)=sqrt(x^2)=|x|=-x
Answer A


sqrt(x^2) = |x| is a rule

since x<0
-x>0
take x=-3 for example and plug in:
sqrt(-(-3)|3|)= sqrt (3*3)= 3

so answer is -x.
A

I don't understand what we need to find here X or the result of equation root(-X*|X|). Please explain me.

You need to find the result of the equation root(-X*|X|).

Why it the -x but is not just x?

GambitOS

On the GMAT, the square root of a number is ALWAYS positive but when you have x^2, x could be positive or negative. In other words,

(x)^1/2 = x
(x)^2 = x or -x

This is a statement of fact from the Official Guide.

Now consider what Matmasi contributed:
since x<0, -x>0

Therefore, the square root of |x| multiplied by -(-x) = x (and remember that on the GMAT square roots are ALWAYS positive).

Remember Matmasi already noted that -x>0, and when you plug in the value of -3 as x into -x you have -(-3) = 3. Therefore -x = 3.

Follow the logic and it will make sense.

Thanks tohellandback and matmasi. This forum rocks!!