Hey aimscore:
I don't want to criticize out of context, as that question may have some surrounding lesson to it that has a lot of value, but you won't see that application of the square root rules on the official GMAT. The very fact that we're discussing it right now demonstrates that it's not a good GMAT question - an intelligent, capable test-taker would be more than justified in selecting the "wrong" answer here, or at least in struggling to determine which application of the rule to choose, and that isn't a proper way to determine which MBA candidates are better prepared.
Here's the general rule of thumb for square roots and their negative/positive solutions:
Whenever you see x^2 = _____ and are asked to solve for x, you have to remember that there's a negative and positive root (unless x is 0). This is the Data Sufficiency application, usually - or really any logical reasoning with roots type applications (problem solving question that ask "which of the following must be / cannot be true" will use the same ideology). If this were a true GMAT problem they'd give you that setup (q^2 = 9) and your answer would be correct.
When they give you the radical sign (sqrt 9 = x), that's more of a calculation-based question in a problem solving context, and there they only want you to use the positive square root. The only reason they'll do this is if they want you to calculate using roots, in which case having multiple +/- possibilities make it impossible to solve, say:
sqrt 32 + sqrt 50
Here, they want you to simplify those and calculate (4 sqrt 2 + 5 sqrt 2 = 9 sqrt 2), and it wouldn't make sense to have the possibility for negatives in there.
The way you're thinking is perfect - it's much more important for you to recognize and keep in mind the first application, because that's the one that can trap you. The second? That one's hard to screw up...it's pretty intuitive that you wouldn't solve four different problems there (+, -; +, +; -, +; -, -), and since the answer choices would all be all positive you're pretty much stuck using the positives.
Summary: Even if it means getting this question wrong, please, please keep thinking the way you're thinking about roots and you'll be in great shape!
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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but for the moment, could u please explain the answer in a little more detail
