√(-x│x│) is ?

[pgarg00]

If x < 0, then

√(-x│x│) is

A. -x
B. -1
C. 1
D. x
E.

√x

I was confused between A and D .. can someone explain ?

[putneyswope]

Originally Posted by pgarg00

If x < 0, then

√(-x│x│) is

Hey pgarg00, I got this one wrong too if its any consolation

Pick a value

x = -1

√(-(-1)│-1│)
√(-1)│-1│)
√(1x1) = 1 or -(-1) or -x

[800Bob]

Originally Posted by pgarg00

I was confused between A and D .. can someone explain ?

How could it be D? The question states clearly that x < 0, and √ never represents a negative number.

[Cippo]

ok, I took the point.

√(-x│x│) =√(-x│x│) if x < 0 -> √(-x -x) = √(x2) = │x │= -x (when x<0) so A.

[anandisonline]

Its D...
√(-x│x│) =√(-x│x│)
if x < 0 =√(-x -x) = x
so answer D...
whats the issue...
"√ never represents a negative number" couldnt get this statement.
Here there is no imaginary nbr consept required

@anadisonline
so why not:
if x=-2 ->
√(-x -x) = √(2. 2) = √(4) = -> this could be -2 which is x, or +2 which is -x?

[800Bob]

Originally Posted by anandisonline

"√ never represents a negative number" couldnt get this statement.

Choice D is impossible. There is no way that √ of anything could equal x, since x is negative.

[800Bob]

Originally Posted by angryMOFO

√(4) = -> this could be -2 which is x

No, √4 cannot be -2.

Official Guide, 11th edition, page 114:

“Every positive number n has two square roots, one positive and the other negative, but √n denotes the positive number whose square is n. For example √9 denotes 3. The two square roots of 9 are √9 = 3 and –√9 = –3.”

[anandisonline]

so in this case answer is E

[800Bob]

Originally Posted by anandisonline

so in this case answer is E

No.

√(-x│x│) = ?

Since x < 0, we can say that |x| = -x:

√(-x│x│) = √[(-x][-x)] = √(x^2)

Now, √(x^2) = |x|. That is, √(x^2) = x if x ≥ 0, or √(x^2) = -x if x < 0. In this case, x < 0, and so...

the answer is -x, choice A.