I guess the best way to solve this question is to plug in values and see how the result features.

Before we do the same, explanation by HongHu is perfect. (Cant post the link to his reply as I am new to the club

)

i.e

Square root of any positive number is a positive numberNow getting back to the actual question:

If x<0, then \(\sqrt{-x*|x|}\) equals:

1. -x

2. -1

3. 1

4. x

5. \(\sqrt{x}\)

Approach:

Since x <0, let use plug in a negative integer as x, for e.g.

Let x = -2 ---- [1]

Hence \(\sqrt{-x*|x|}= \sqrt{-(-2)*|-2|} = \sqrt{2*2} = \sqrt{4}\) ---- [2]

Now as per the discussion going on, the point of disagreement is that \(\sqrt{4}\) = 2 or -2. But as stated by HongHu, we would consider \(\sqrt{4}\) = 2 only! The reason for this conclusion is that the radical sign used in \(sqrt{x}\) is used to show the positive square root of a number x.

Therefore \(\sqrt{4} = 2\) ----

[3]Now as per Equation [1] marked above, x = -2 which can also be written as -x = 2 ---- [4]

Hence if we subsitute the values of \(\sqrt{4}\) from equation 2 ( i.e. \(\sqrt{-x*|x|}\) ) and value of 2 from equation [4] ( i.e. -x )... in equation [3], we get the following result:

\(\sqrt{-x*|x|} = -x\) and hence the correct answer is

1This approach can be verified by another question which featured in the GMAT prep exams...

If \(x \neq 0\), then \(\frac{\sqrt{x^2}}{x}\) equals:

1. -1

2. 0

3. 1

4. x

5. \(\frac{|x|}{x}\)

Approach:

In this question, we don't know whether x is negative or positive. Hence \(\sqrt{x^2}\) is always equal to |x|. Reason for the same is: x is a variable here and we dont know the exact value.

The absolute value sign is needed when we are taking the square root of a square of a variable, which may be positive or negativeTherefore in this situation, the answer would be

5Hope this helps!

Cheers!

JT

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Cheers!

JT...........

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