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if x<0, then (-x|x|)^1/2 is what?

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by tohellandback » Tue Sep 01, 2009 6:41 pm
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
The powers of two are bloody impolite!!
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by Matmasi » Wed Sep 02, 2009 8:19 am
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
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by GambitOS » Thu Sep 03, 2009 2:48 am
I don't understand what we need to find here X or the result of equation root(-X*|X|). Please explain me.
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by Matmasi » Thu Sep 03, 2009 2:51 am
You need to find the result of the equation root(-X*|X|).
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by GambitOS » Thu Sep 03, 2009 3:44 am
Why it the -x but is not just x? :?
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by ogbeni » Sat Sep 05, 2009 5:59 am
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!!
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