As in 1.9 of Milne's note Algebraic Groups, it is said that if $G/k$ is a geometrically reduced group scheme, then for a field extension $k'$ of $k$, $G(k')$ is dense in $G$ if and only if $G(k')$ is dense in $\vert G_{k'} \vert$. Here $G(k')$ is dense in $G$ means that if a closed subscheme $Z \subset G$ satisfies $Z(k') = G(k')$ then $Z=G$.
The if part is easy. But why the only if part is true?