First of all, the square root of a negative number can't be a real number right, and isn't one of the assumptions on GMAT that all numbers are real?
That's true. But you don't have to compute the square root of a
negative number to realize that it's always true that
sqrt(x)^2 = x
In contrary to
sqrt(x^2) = |x|
Second, isn't III implicit of both I&II???
Well it is, but to realize that has been a part of the question.