If x < 0, then sqrt(-x|x|) is

[Guest]

Please refer to the attached image.

The answer is -x.

a) how is the answer to a sqrt negative?

b) isn't the sqrt of (-x) * (-x) = sqrt of x^2 = x.

What am I missing?

Thank you.

[StaceyKoprince]

Really confusing. The question begins by telling us that x is negative. The second term, [x] (those are supposed to be absolute value signs) actually becomes -x. Think about it - absolute value means the number becomes positive. x by itself indicates a negative number. So to indicate the positive version of the negative number, I have to put another negative sign in front of it, to cancel out the negatives.

That leaves me with SQRT(-x*-x). The square root of that is -x, which is not actually a negative number - it's a positive number. (Remember, again, that x is negative.)

[Guest]

those tricksters!!

[mrohekar]

Another tip : Square root of a negative number will have an 'i' (imaginary number) in its answer

eg. square root of -16 = 4i.

Hence if the answer choices have a -ve number without an 'i' they can be straight away ruled out. Additionally I dont think GMAT test imaginary numbers.

Hence if you get a negative number under the square root sign check to see if the answer choices have an 'i' or you have made a mistake.

[Harish Dorai]

Given X is negative.

So (-X) is positive.
|X| is always positive.

So (-X) multiplied by |X| is also positive which is also equal to Square of X. Its square root can be -X or +X

Since they have given the Radical sign and there is no negative sign before the radical sign the resultant expression should be Positive. For that it has to be (-X) (Because X is negative from the first statement).

Hope it helps

[Guest]

"have a -ve number"

Don't understand the lingo, what does "ve" or "-ve" stand for?

thanks.

[Guest]

"have a -ve number"

Don't understand the lingo, what does "ve" or "-ve" stand for?

thanks.

-ve : negative number
ve : positive number

[StaceyKoprince]

The GMAT doesn't test imaginary numbers. You'll never see an i indicating an imaginary number on the test.

[vinversa]

IF x<0, then SQRT(-x.|x|) is


|x| = -x if x<0 (GMAT given rule)
Then we get SQRT(-x.-x)
SQRT(x^2)
+/-x

But since x<0 (given)

We pick -x as answer

[sudaif]

i like vinesa's method the best
very often, i've made the mistake of cancelling out the the square with the overhanging square root sign without considering the positive negative sign that results.

also, another way to quickly solve such a tricky question would be to pick numbers.
if you take x=-1, you get answer =1
if you take x=-2, you get answer =2
the result in itself is the negative of x...and results in a positive number.

[debmalya.dutta]

sqrt(-x|x|) = sqrt(-x*-x) because |x| = -x when x<0
= sqrt(+x^2)
= +x or -x
But question stem says x<0..hence sqrt(-x|x|)=-x

[RonPurewal]

by far the easiest way to solve this problem is to pick your own number for x.
the prompt implies that this will work for all values of x < 0, so it's guaranteed that you'll be able to pick any such value.

let's say x = -4.
then the prompt becomes √(-(-4)(4)), or √16 = 4.
(a) 4
(b) -1
(c) 1
(d) -4
(e) impossible

done. answer (a).

[gmataker]

[*]|x| -> Absolute value of x
[*]Given, x<0

So, after substituting x = -x, the equation √-x|x| can be re-written as

√-(-x)|-x|
= √x.x (because |-x| = x) (DONT stop here)
=√x²
= +x or -x

But because x<0 (given) , we choose the answer as -x. I guess the mistake most people make is to ignore the given condition of x being negative and assume √x.x = x

Is this a correct approach?

[gokul_nair1984]

[*]|x| -> Absolute value of x
[*]Given, x<0

So, after substituting x = -x, the equation √-x|x| can be re-written as

√-(-x)|-x|
= √x.x (because |-x| = x) (DONT stop here)
=√x²
= +x or -x

But because x<0 (given) , we choose the answer as -x. I guess the mistake most people make is to ignore the given condition of x being negative and assume √x.x = x

Is this a correct approach?

Correct :)

[tim]

you don't want to substitute x=-x. that is an incorrect statement. the better way to do this is to say x = -|x|. now the negatives cancel out and you have root(|x||x|). well, |x||x| = x^2 so it is root(x^2), which you should memorize is equal to |x|. since x<0, |x| is a positive number, in other words -x..