There is an 'easy' way to work out the radical of an ideal in case this is principal (which in your case it is):
Let where is its factorization into irreducibles, then
To prove this let then there exists such that ie. for some polynomial , by the uniqueness of a factorization in a polynomial ring (over a field at least) the must appear in the factorization of , and so . On the other hand if then .