When you multiply any number by itself, the result is always positive. You cannot take any real number and square it to get something negative. The square root of -36 is 6i.
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A Square Root is one of the two equal factors of a number.
Yes. Every perfect square has two roots: one positive and one negative.
And its negative counterpart.
No there is not. If you are looking for prime factors of a number and you get to the square root of that number you can stop. Yes, there is. If an integer is not itself a prime, then one of its factors will be less or equal to its square root and the "co-factor" will be greater than or equal to the square root. But both cannot be greater than the square root so, when searching for factors, you can stop when you reach the square root.
A square root.