  In 1977, Adleman, Manders and Miller had briefly described how to extend
their square root extraction method to the general $r$th root extraction over
finite fields, but not shown enough details. Actually, there is a dramatic
difference between the square root extraction and the general $r$th root
extraction because one has to solve discrete logarithms for $r$th root
extraction. In this paper, we clarify their method and analyze its complexity.
Our heuristic presentation is helpful to grasp the method entirely and deeply.
