Let $k$ be a field. Let $A$ be a commutative algebra over $k$. We say $A$ is geometrically reduced over $k$ if $A\otimes_k k'$ is reduced for every extension $k'$ of $k$.
Let $K$ be an algebraic extension of $k$. It is well-known that $K$ is geometrically reduced over $k$ if $K$ is separable over $k$. Conversely suppose $K$ is geometrically reduced over $k$. $K$ is separable over $k$?