prove that this ideal is radical

Question

Let $A=\mathbb k[x,y,z]$ and let the ideal $$ I=(z-1,x^2-y).$$ I need to find $rad(I)$ but i don't know how.

I think that this ideal is radical but I don't know good criteria for doing that =(

Answer 1

$I$ is a prime ideal since clearly $k[x,y,z]/(z-1,x^2-y) = k[x]$.