Hello all,

I was wondering if anyone could help me answer the question: find ideals $\displaystyle I,J$ of $\displaystyle k[x_1,\ldots,x_n]$ such that $\displaystyle \sqrt{I+J} \not= \sqrt{I} + \sqrt{J}$, where k is an algebraically closed field (i.e. find a counterexample) Can anyone give me a hint about how to go about this? I tried messing around with $\displaystyle \mathbb{C}[x] $ but I can't really work anything out.

Any help would be appreciated, thank you