Solution
= Solution
The <radical of an ideal> $I$ in a commutative ring $A$ is $\sqrt I=\{a\in A:a^m\in I\text{ for some }m\geq1\}$. It is an ideal: if $a^m,b^n\in I$, every term of $(a+b)^{m+n}$ has either at least $m$ factors $a$ or at least $n$ factors $b$, so the sum belongs to $I$. Also $(ca)^m\in I$ for every $c\in A$, and additive inverses preserve the defining condition.