radical of an ideal

Question

Let $R$ be a commutative ring with identity and $I$ a proper ideal of $R$. We define $L$-radical of $I$, denoted by $\sqrt[L]{I}$, the intersection of all primary ideals of $R$ containing $I$. It is clear that $\sqrt[L]{I\cap J}\subseteq \sqrt[L]{I} \cap \sqrt[L]{J}$ where $I$ and $J$ are proper ideals of $R$. I'm looking for a counterexample to show that the reverse inclusion not true, in general.