  In this article we derive an approximation inequality for continued radicals,
generalizing an inequality of Herschfeld for continued square roots to
arbitrary radicals, which is useful in exploring convergence issues and
obtaining convergence rates. In fact, we generalize this inequality further to
encompass the more general continued power forms. We demonstrate the use of
this inequality by obtaining estimates for the convergence rates of several
continued radicals including the famous Ramanujan radical.
