It easy to show that √2 is an irrational number

So is the square root of any non-square number.

Prove that √22 is an irrational number, providing a reasoning applicable to any random-chosen non-square integer.

sgrt(k) is rational if and only if it equals a/b, where a and b are integers.

Then k =a^2/b^2

and k*b^2 = a^2.

This is only possible if integer k is also square.

Therefore, sgrt(k) is rational if and only integer k is a square.