Period of $f(x)=\sin(4x)+\cos(x\sqrt{2})$

Question

I have $f:\mathbb{R}\rightarrow \mathbb{R}, f(x)=\sin(4x)+\cos(x\sqrt{2})$ and I need to find the period of this function. I found that the period of $\sin(4x)=\pi/2$ and the period of $\cos(x\sqrt{2})=\pi\sqrt{2}$. Why doesn't this function have a period and how can I approach the exercise?