probability - Finding the PDF of the sum of two independent standard normal variables

The question asks for the PDF of

$$Y=(X_1)^2+(X_2)^2$$
Given that $X_1$ and $X_2$ are independent standard normal variables.
I found that the pdf for $(X_i)^2$ is
$$f_{X^2}(x) = \frac{1}{2\pi}e^{-x/2} x^\frac{1}{2}$$ for $x \geq 0$.
But I'm stuck on what to do next.