1. The problem statement, all variables and given/known data prove that if n is a natural number greater than 0, then sqrt(n^2 + 1) is not a natural number. 2. Relevant equations 3. The attempt at a solution I can't tell if I am right, which probably means that I am not. Assume sqrt(n^2+1) is a natural number. Then there is a natural number j such that j = sqrt(n^2+1). Thus j^2 = n^2 + 1. Then, I am stuck. It seems too easy to prove, is there some little trick I am missing.