Referring to Exercise 34, show by examples that for proper ideals N of a commutative ring R, 

a. √N need not equal N 

b. √N may equal N.

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.