Question

both the square as well as the square root of thus whole number is a rational number.
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Answer 1

Answer:

If the square root of an integer is itself an integer, then by definition it is rational - If the square root is not integer, then it must be irrational.

Put another way the only integers for which the square root of an integer n can be rational is if n is a perfect square - that is n=x∗x where x is an integer.

The same rules applies to any integer root (say cube root, 4th root etc).

The only way I know to test a number for being a perfect square is to try to find it’s square root - with small numbers it is easy, it can be more time consuming with larger numbers. Remember all you need to is prove it is not a perfect square - that being the case then the square root must be irrational.