The product of negative three squared is nine. To square a number means to multiply that number by itself, and multiplying two negatives together yields a positive number, as About.com explains. Negative three times negative three, therefore, is nine.
A negative number is never a perfect square. The smallest perfect square possible is zero because zero times zero is zero. The square root of a number is potentially either positive or negative. For example, the square root of nine is three or negative three. Squared odd numbers always have an odd result, and squared even numbers always yield an even result. In this case, negative three is odd, and its square is nine, which is also odd.