This all has to do with agreed-upon notation. From the Official Guide:

A square root of a number n is a number that, when squared, is equal to n. Every positive number n has two square roots, one positive and the other negative, but √n denotes the positive number whose square is n. For example, √9 denotes 3.


Cheers,
Brent

Hi All,

There's actually a rather simple way to deal with this issue. Focus on what the prompt GIVES YOU to work with.

If you're given a square root sign, then you are responsible for the POSITIVE answer ONLY.

If you're given a squared term (e.g. X^2 = 25), then you are responsible for BOTH the POSITIVE and NEGATIVE answers.

By extension, if you're given a quadratic (e.g. X^2 +2X - 3), then you're responsible for BOTH answers (regardless of whether they're positive or negative).

In questions involving logical restrictions (geometry, etc.), there's no such thing as a "negative side length", which is why the Pythagorean Theorem is concerned with just the positive results.

GMAT assassins aren't born, they're made,
Rich