Let $I, J$ be ideals in a commutative ring with identity $R$. Define the quotient ideal $(I : J)$ by $$(I : J)=\{x\in R : xJ\subseteq I\}.$$

Define the radical $r(A)$, of an ideal $A$ of $R$ by

$$r(A)=\{x\in R\;:\;x^n\in I, \;\;for\;some\;n>0\}.$$

My question is: There is some link between $r[(I : J)]$ and the two radicals $r(I)$ and $r(J)$?

Let $I, J$ be ideals in a commutative ring with identity $R$. Define the quotient ideal $(I : J)$ by $$(I : J)=\{x\in R : xJ\subseteq I\}.$$

Define the radical $r(A)$, of an ideal $A$ of $R$ by

$$r(A)=\{x\in R\;:\;x^n\in A, \;\;for\;some\;n>0\}.$$

My question is: There is some link between $r[(I : J)]$ and the two radicals $r(I)$ and $r(J)$?