Yes and no.
It depends on your definition of square root. By the actual one, yes. All non-negative numbers have a square root. That square root might be irrational but it has a square root, nonetheless. 10 isn't a square number because there's no integer that can be squared to make ten but 10 definitely has a square root: 3.16227766.......
If by square root you mean an integer square root, then no. If a number has an integer as its square root then you could square that integer to get the number, making it a square number.
They are called real numbers. Negative square roots must be complex numbers.
No. The square roots of perfect squares are rational.
There are no real square roots of -256. But using complex numbers the square roots of -256 are 16i and -16i.
There are no following numbers!
imaginary numbers. but no, not really.
No. The square roots 8 are irrational, as are the square roots of most even numbers.
Numbers with square roots that are whole numbers
They are called real numbers. Negative square roots must be complex numbers.
No. The square roots of perfect squares are rational.
There are no real square roots of -256. But using complex numbers the square roots of -256 are 16i and -16i.
Negative numbers have no real square roots. In terms of complex numbers, the square roots of 43 are +j6.5574 (rounded) and -j6.5574 (rounded)
No, not all square roots are rational numbers. A rational number is a number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. Square roots that are perfect squares, such as √4 or √9, are rational numbers because they can be expressed as whole numbers. However, square roots of non-perfect squares, such as √2 or √3, are irrational numbers because they cannot be expressed as a simple fraction.
There are no following numbers!
Square roots of negative numbers ARE possible. I guess you haven't been introduced to "imaginary numbers" and the letter "i".
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.
Negative numbers do not have "real number" square roots.However, they will have two roots (when using imaginary numbers) as do other numbers, where a root including i(square root of -1) is positive or negative.
The square roots of a number are numbers and, as numbers, they are not capable of doing anything.