perfect squares
They are called real numbers. Negative square roots must be complex numbers.
Any negative number, and infinity. However, a number (called "i") was created to represent the square roots of negative numbers.
They can, but they are called imaginary numbers. This is because a "square" of something is the number that, when multiplied by itself, will equal the first number. A negative multiplied by a negative equals a positive, and positives can't turn into negatives on their own, so there are no square roots of negative numbers.
A square root is not a number system. Square roots of non-negative numbers may be rational or irrational, but they all belong to the set of real numbers. The square roots of negative numbers do not. To include them, the number system needs to be extended to the complex numbers.
perfect squares
They are called real numbers. Negative square roots must be complex numbers.
A number with a square root is still a number. So the answer is all of them.
The square roots of a number are numbers and, as numbers, they are not capable of doing anything.
Any negative number, and infinity. However, a number (called "i") was created to represent the square roots of negative numbers.
There is no specific name but they comprise the set of non-negative numbers other than perfect squares.
They can, but they are called imaginary numbers. This is because a "square" of something is the number that, when multiplied by itself, will equal the first number. A negative multiplied by a negative equals a positive, and positives can't turn into negatives on their own, so there are no square roots of negative numbers.
Rational numbers whose square roots are whole numbers are themselves whole numbers. They are called square numbers, e.g. 1, 4, 9, 16, 25 and so on.
Every whole number
A square root is not a number system. Square roots of non-negative numbers may be rational or irrational, but they all belong to the set of real numbers. The square roots of negative numbers do not. To include them, the number system needs to be extended to the complex numbers.
There are none. Negative numbers don't have square roots. Well, they do, but they are known as imaginary numbers, and there is no way to determine them. A square root of a number is a number you can multiply by itself and get the original number. There is no number you can multiply by itself to get a negative number, but every positive number has two square roots of the same absolute value.
They are called perfect squares.