tnaim wrote:this might seem like a simple question but then if you look at this example from GMATprep:
f x<0, then √(-x|x|) is
A. -x
B. -1
C. 1
D. x
E. √(x)

official answer is A





if you actually take -5 as an example to plug to the √(-x|x|) , you will see that you will end up with √25 and here the question becomes √25 is +-5 or just 5?
I have searched the internet for quite a bit and found conflicting opinions
Ron here says that √25 is just 5
https://www.manhattangmat.com/forums/if- ... t8539.html
enough resources on the internet say that √25 is +-5
https://mathforum.org/library/drmath/view/57877.html

my question thus is: what is √25? are there rules for when we consider √25=5 and other rules when √25=+-5? or is there just one answer all the time with no exceptions!!
thanks for the help!

• 1) if the GMAT presents a value as a root, that value is positive. If you're told that z=root(36), then z=6. If the GMAT already shows the value under a root, you're dealing with a positive root

• 2) If the GMAT presents the square (instead of the root), then you must consider both positive and negative solutions. If the GMAT states that z^2=36, then z can be +-6. In this case, z is not presented as a root. Instead, you're simply told that its square is 36.