Let x and y be identically distributed variables have density function $\displaystyle f(u)=\frac{e^{\frac{-u^2}{2}}}{(2\pi)^\frac{1}{2}}$

find the density function of z=x^2+y^2

i have an answer given as $\displaystyle g(z)=.5e^{\frac{-z}{2}}$ for $\displaystyle z\geq 0$

but I cannot seem to get that answer, thanks in advance