Prove that any power of $10$ can be written as sum of two squares

Question

I do know various techniques to solve this problem, but I need an elementary solution which can be explained to a fifth grader (that is, with as little algebra as possible, no modulo arithmetic).

Answer 1

$3^2+1^2=10$, $8^2+6^2=100$, $30^2+10^2=1000$, $80^2+60^2=10000$, $300^2+100^2=100000$ etc.

Answer 2

If $n=2m$ is even, then $$ 10^n=(10^m)^2+0^2$$ while if $n=2m+1$ is odd, then $$ 10^n=(9+1)\cdot 10^{2m}=(3\cdot 10^m)^2+(10^m)^2$$