How to check if the following function is periodic or not?

Question

I have $f(x)=\sin(x)$ so it has a period of $2\pi$, and I have $g(x)=\sin (\sqrt{2}\,x)$ so it has a period of $\sqrt{2}\pi$. I also know that a function $f(x)$ is periodic if $f(x)=f(x+p)$, now I want $h(x)=f(x)+g(x)$. How do I check whether $h(x)$ is periodic or not?

Answer 1

Hint: assume that it is periodic, with period $P$. Then $P$ must be an integer multiple of both $\sqrt{2}\pi$ and $2\pi$.