Yes, it is +3 or -3
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Yes. The square of a whole number is always a whole number. For example, 3 squared is 9, so the square root of 9 is 3. What you never have, is the square root of a whole number being a fraction that is not a whole number. The square root of a whole number is either a whole number or an irrational number. For example, the square root of 2 is irrational, because there are no 2 whole numbers a and b such that a/b squared is 2. This is not terribly difficult to prove, but I have already said too much; I have answered your question.
9
Yes. For example, the square root of 1/9.
For a number to be a perfect square, the number's square root has to be a whole number. 9 is a perfect square because its square root is a whole number, 3. If the square root of the number is a decimal, then it is not a perfect square. For example, 13 does not divide evenly so it not a perfect square.
3 is the square root of 9. 9 is a square number. 9 is the square root of 81. 81 is a square number.