Hello experts,

Given that there is a commutative ring R and 2 ideals I and J, also given that I is included in J

I need to prove

2. These are both immediate from the definition of the radical of an ideal. Do you understand the definition? Have you tried to write down precise statements of (1) and (2) in terms of that definition? That's essentially all this problem calls for.

3. A tiny hint:

$I\subset \textrm{rad}(I)$