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The square root of 4 is both 2 and "something else." Do you see why?
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Wrong. The square root of 4 is 2 and only 2. If the question were worded "what number squared is equal to 4?", then you would be right; there would be multiple answers.
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The definition of the square root function is the inverse function of f(x) = x*x. Which is basically - exactly as you worded it - what number squared is equal to 4?
So the square root of 4 is -2 and 2.
From
http://mathworld.wolfram.com/SquareRoot.html : "Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3".
In all fairness it does also say "In common usage, unless otherwise specified, "the" square root is generally taken to mean the principal square root.".
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The square root of a number CANNOT be both positive and negative. If it could, why would the quadratic equation contain "-b + or - the SQRT". It would be redundant to state "+ or -" if a SQRT could be both at the same time! And I don't know anyone serious about math that would say the square root of 4 is -2. If there's no negative sign, you assume it's the principle square root. If you're looking for the negative square root of a number, you put a negative sign before the square root. If the answer is both, you put a positive and negative sign in front of it. Maybe we need to get BruceZ in here.
This will be my last post on this topic as I already feel we've hijacked this thread enough.