If x < 0, the the square root of

[alysekilleen]

If x < 0, then the square root of (-x multiplied by the absolute value of x)* is:

a) -x
b) -1
c) 1
d) x
e) square root of x

*the full term of -x multiplied by the absolute value of x is together under the square root sign.

The answer is a.

Explanation from an instructor would be helpful.

Thank you!

[james.jt.wu]

Hi There,

I am not an instructor but hope I can help out. You can do this problem in two ways. First, and probably easier way, is to take any negative number and just plug into the question and answer choices and see which one matches.

Second way is algebra, which is not preferrable for complex absolute value questions such as this question if you are short on time. But if you want to do it that way, it would be as follows:

Question: If x < 0, square root(-x*|x|) is equal to what expression?

The key here is to realize that |x| = x when x>0, and |x| = -x when x <0 (that is the definition of absolute values).

Since x < 0, the expression under the square root now becomes:
-x * -x = x^2. So now you are taking square root of (x^2), which is actually |x|. (this is one of the things you should memorize)

As per before, |x| = x when x>0, and |x| = -x when x<0. Since x<0, the express simplifies to -x, which is Answer A.

Hope this helps :) Again, plug numbers if you can... fastest way to do it!

[alysekilleen]

Thank you for your reply.

I don't understand why the answer would not be d (x).

if we took the square root of -5 squared, would that then equal -5? If you square -5 you get +25 and the square root would be 5. Correct?

I thought that two negatives multiplied would lead to a positive. Further, in the original scenario, the numbers multiplied are positive (- -x * absolute value of x) which should again yield a positive.

Or, is it the case that anytime you take the square root of an unknown variable the answer is either + or negative, but not determined without further evidence.

[rambabu]

Hi There,

I am not an instructor but hope I can help out. You can do this problem in two ways. First, and probably easier way, is to take any negative number and just plug into the question and answer choices and see which one matches.

Second way is algebra, which is not preferrable for complex absolute value questions such as this question if you are short on time. But if you want to do it that way, it would be as follows:

Question: If x < 0, square root(-x*|x|) is equal to what expression?

The key here is to realize that |x| = x when x>0, and |x| = -x when x <0 (that is the definition of absolute values).

Since x < 0, the expression under the square root now becomes:
-x * -x = x^2. So now you are taking square root of (x^2), which is actually |x|. (this is one of the things you should memorize)

As per before, |x| = x when x>0, and |x| = -x when x<0. Since x<0, the express simplifies to -x, which is Answer A.

Hope this helps :) Again, plug numbers if you can... fastest way to do it!

from my understanding, |x| = x when x<0 or x>0. correct me if i am wrong.

the expression comes down to square root x^2, which will result in x or -x. from the given condition x<0, i will drop x but pick -x as anwer.

[gokul_nair1984]

@alysekilleen.. the sqrt(25) =+/-5 not only +5..

eg: x^2= 25 ...=> x=+5 or-5

|x|=+x when x is positive and |x|=-x when x is negative ...


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

Plug in x=-2... we get,

sqrt(-(-2)|-2|)=sqrt(2*-(-2)= sqrt(4)=+2 or -2 ... but it is already given that x<0. Therefore, x=2 or (-x)

[RonPurewal]

look here:

if-x-0-then-sqrt-x-x-is-t903.html