We formulate the Root Extraction problem in finite Abelian $p$-groups and
then extend it to generic finite Abelian groups. We provide algorithms to solve
them. We also give the bounds on the number of group operations required for
these algorithms. We observe that once a basis is computed and the discrete
logarithm relative to the basis is solved, root extraction takes relatively
fewer "bookkeeping" steps. Thus, we conclude that root extraction in finite
Abelian groups is no harder than solving discrete logarithms and computing
basis