Square root of one plus eight times a perfect number

Statement

For every even perfect number $N$ the value $\sqrt{1+8N}$ is an integer (each even perfect number is triangular). Verify this for $N=8128$.

Solution

$1+8\cdot 8128=1+65024=65025=255^2,$ hence $\sqrt{1+8\cdot 8128}=\boxed{255}.$