What is the relationship of the ideal √N of Exercise 34 to the nilradical of R/N (see Exercise 30)? Word your answer carefully.

Data from Exercise 34

Let R be a commutative ring and N an ideal of R. Show that the set √N of all a ∈ R, such that aⁿ ∈ N for some n ∈ Z⁺, is an ideal of R, the radical of N.