A note on ``Zippel denesting'' (Q1186700)

\textit{R. Zippel} [J. Symb. Comput. 1, 189-210 (1985; Zbl 0574.12002)] gave a criterion for the denesting of a given radical, but assumed implicitly that a certain field was a Galois extension of another. In the present note Zippel's result is proved with the condition made explicit, and the converse of Zippel's result is also proved. It is shown how the result may be used systematically to obtain a denesting, though not necessarily the minimal denesting.