Compute the radical of the ideals $(x-3)$, $((x+1)^3)$

Question

Let $R$ a commutative ring. I know that $\sqrt I=\{r\in R\mid \exists n: r^n\in I\}$, but I don't know how to compute $\sqrt I$ when $I$ is given.

For example, how can I compute $\sqrt{(x-3)}$ and $\sqrt{((x+1)^3)}$?

By the way, what does $(x,y)^2$ mean ? (it's from primary decomposition).

Answer 1

Hint $\sqrt{((x-a)^n)}=(x-a)$ is an immediate consequence of the definition. (Prove it by double inclusion)