Yes. It is an Irrational number, but all Irrationals are Real rumbers.
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It is not the square of a whole number; but it is the square of a real number. If you calculate the square root of 23, you will get a real number. That real number times itself will equal 23. But the square root will not be a simple whole number. It will have an endless decimal fraction.
There is no real number [square] root of a negative number. There is a real cube root and a real fiftth root etc, but root, by itself, implies square root.
a prime square
The answer is 961. The square root of 961 is 31, which is a prime number.
The square root of any positive real number (as in this case) is a real number. (Such square roots are usually irrational.)The square root of a negative real number, such as the square root of -15, is an imaginary, and therefore also a complex, number.