Sage Pearce-Higgins wrote:I think I know what's confusing. You've seen a bunch of problems in which you have to be careful to consider negative solutions to square roots. For example, if we're told that x^2 = 81 in a DS problem, then that's not sufficient information to know x (since there are two solutions). However, when a root sign is given in GMAT, we only need to consider the positive root. Take a look at this post:

https://www.manhattanprep.com/gmat/foru ... ml#p117271

But here the question stem does not contain any root sign. Nor we can infer positive/negative.

I mean, if I write that the side of a square is sqrt(4), then I obviously mean the positive solution (the side is 2, not -2, because a side must have a positive length).

But here the question stem does not contain any root sign. However:

The square root of 4 is 2 or -2, so there's a solution that satisfies the second equation. However, we don't need to worry about the negative solution here (read on).

Here you are theoretically right, but as Ron said in the post you cited, mathematical functions must be unambiguous.

In fact, if you look up square root in Wikipedia it reports what I have learned in school:

Every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, which is denoted by √9 = 3, because 32 = 3 • 3 = 9 and 3 is nonnegative.

So the square root symbol only denotes the positive solution, and not the negative solution. That is to say, a mathematical function must output a unique value.

In your example, how would you know how to pair the negative and positive sign?

So in the example in question, this is what I would have done:

(a+b)/4 = (x+y)^2 => sqrt{(a+b)/4} = |x+y| = (x+y) or (-x-y)

So I am a bit confused: when we should take into consideration the positive/negative sign and where not?

What is "Latex"?

Latex is a typeset system. It is used, among other purposes, in some mathematical forums to render equations correctly (instead of seeing sqrt(2)/2, you see the actual square root sign and the fraction)