### Explain the Proof Step-by-step : Irrational Function

Recall that a perfect sqaure is a natural number n such that n = (k^2), for some natural number k. Theorem. If the natural number n is not a perfect square, then n^(1/2) is irrational. Proof. S(1): Suppose n^(1/2) = r/s for some natural numbers r and s. S(2): We may assume that r and s have no prime factors in common,