A Spigot-Algorithm for Square-Roots: Explained and Extended
Abstract
This work presents and extends a known spigot-algorithm for computing square-roots, digit-by-digit, that is suitable for calculation by hand or an abacus, using only addition and subtraction. We offer an elementary proof of correctness for the original algorithm, then present a corresponding spigot-algorithm for computing cube-roots. Finally, we generalize the algorithm, so as to find r-th roots, and show how to optimize the algorithm for any r. The resulting algorithms require only integer addition and subtraction.
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