if x < 0, then sqrt (-x*|x|)) is
A) -x
B) -1
C) 1
D) x
E) sqrt (x)
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GMAT prep problem 1
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shri_ankur
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mschling52
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I think it's A, -x.
Since x is negative, -x is positive and -x = |x|.
Therefore, -x*|x| = (|x|)^2. Then, plugging this into the original problem,
sqrt((|x|^2)) = |x| = -x
You could solve this by plugging in a negative number and seeing what you get. For instance, say you chose -4 to be x. Then,
sqrt(-x*|x|) = sqrt(-(-4)*|-4|) = sqrt(4*4) = sqrt(16) = 4 = -x
Since x is negative, -x is positive and -x = |x|.
Therefore, -x*|x| = (|x|)^2. Then, plugging this into the original problem,
sqrt((|x|^2)) = |x| = -x
You could solve this by plugging in a negative number and seeing what you get. For instance, say you chose -4 to be x. Then,
sqrt(-x*|x|) = sqrt(-(-4)*|-4|) = sqrt(4*4) = sqrt(16) = 4 = -x
