Is this an affine surface? I have to prove that the surface $Z(xy^2-z^2)$ in the affine space is a rational one, where the base field is the complex one. Is it right to use the morphism $t \rightarrow (t,t,t^{3/2})$ with the projection over the first component for the inverse? 
Thank you.

Recall the definitions. Algebraic geometry deals with polynomials, so $t^{3/2}$ isn't well defined here (actually also complex root functions are multivalued and therefore aren't really functions).
Hint: Consider the open subvariety $Z(xy^2-z^2) \setminus Z(y)$. Show that it is isomorphic to an open subvariety of $\mathbb{A}^2$.
