prove that if n is a natural number greater than 0, then sqrt(n^2 + 1) is not a natural number.
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.