# Question

Why can’t I take the square root of both sides to see if statement 1 and 2 are the same? Although, this leaves me to choose the wrong answer, I was just wondering why taking the square root of both sides is not allowed.

# Answer

The problem is that when we take the square root of something like this, we have to consider both the positive *and* negative square roots. So if we square both sides of this inequality, we actually get *two* resulting expressions:

x + y < x - y

and

-(x + y) < -(x - y)

which simplifies to:

x + y > x - y

So overall, we are left with these *two* expressions, meaning that Statement 1 is not exactly the same as Statement 2.

# Link

http://gmat.magoosh.com/questions/969

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