We work with a natural notion of the (noncommutative real) zero set of a left ideal in . The vanishing radical of is the set of all which vanish on . The earlier paper (Cimpri膷 et聽al. [6]) gives an appropriate notion of and proves when is a finitely generated left ideal, a free -Nullstellensatz. However, this does not tell us for a particular ideal whether or not , and that is the topic of this paper. We give a complete solution for monomial ideals and homogeneous principal ideals. We also present the case of principal univariate ideals with a degree two generator and find that it is very messy. We discuss an algorithm to determine if (implemented under ) with finite run times and provable effectiveness.