Imp Funda - Please Help

[rainmaker]

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

A: -x
B: -1
C: 1
D: x
E: sqrt(x)

Please explain your answers.

Thanks

[gmatv09]

IMO D

|x| = x
-x |x| = x^2 (-x = x since x<0)

sqrt(x^2) = x

[rainmaker]

Nope. That's what I got. That's incorrect

[divyalr]

Its a deceiving question.

to evaluate sqrt(-x|x|)

Take an example x= -4( x<0)

sqrt(-(-4) * |-4|) = sqrt(4 *4)= sqrt(16) = 4 (-x)

Answer is A

[ssuarezo]

Its a deceiving question.

to evaluate sqrt(-x|x|)

Take an example x= -4( x<0)

sqrt(-(-4) * |-4|) = sqrt(4 *4)= sqrt(16) = 4 (-x)

Answer is A

Hi:
you have x=-4, but sqrt(16) = +4, no way u get -4 as a square root.

IMO A, but for another reason, (-x|x|)=-X^2, so sqrt(-X^2) = -X, Am I wrong? What's the OA?
Thanks

[divyalr]

Its a deceiving question.

to evaluate sqrt(-x|x|)

Take an example x= -4( x<0)

sqrt(-(-4) * |-4|) = sqrt(4 *4)= sqrt(16) = 4 (-x)

Answer is A

Hi:
you have x=-4, but sqrt(16) = +4, no way u get -4 as a square root.

IMO A, but for another reason, (-x|x|)=-X^2, so sqrt(-X^2) = -X, Am I wrong? What's the OA?
Thanks

I did not get -4 as the square root. All I am saying is sqrt(16) = +4 ( its a negative of (x=-4) : - (-4)) which leads to (-x) Answer A

[Ludacrispat26]

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

A: -x
B: -1
C: 1
D: x
E: sqrt(x)

Please explain your answers.

Thanks

This is actually pretty simple.

Let x=-1

=sqrt (-(-1)*|-1|)
=sqrt (1*1)
=sqrt (1)
=1, which is -x

Let x=-2

=sqrt (-(-2)*|-2|)
= sqrt (2*2)
= sqrt (4)
= 2, which is -x

IMO A

[uttam.albela]

According to OG, When you say sqrt(p*p) whether p is negative or positive, the only answer is |P|.

if you say - (sqrt(p2)), then the answer is - |P|.

So sqrt(-x * |x|) = |X| = - x

Please refer OG maths fundamentals. sqrt(9) = 3 only.

-3 is wrong.

-sqrt(9) = -3

[rainmaker]

The answer is A.

divyalr, Ludacrispat26 explanation seems good

[lunarpower]

many of the earlier posters have the easiest solution here.
since there are variables littered all over the answer choices, plugging in your own numbers is the best way to go here if you don't immediately understand the textbook method.
if you plug in ANY negative value for x, other than -1 (which will leave both (c) and (a) standing), you will instantly eliminate all answers other than (a).

this is what is done in the post by "ludacrispat26", although that poster makes the mistake of plugging in -1 as the first choice. that poster also doesn't show the trial and elimination of the answer choices.

--

by the way:

the use of "√" to represent only the positive square root is not just a gmat convention; this is an absolutely universal convention throughout ALL of mathematics.
√9 is just 3 (not 3 or -3). √16 is just 4. etc.
if x is a variable, then √(x^2) must be the positive square root. hence, √(x^2) = |x| for ALL values of x.

in this problem, since x is a negative number, |x| simplifies to -x.