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arXiv · 2312.15338

A Spigot-Algorithm for Square-Roots: Explained and Extended

Mayer Goldberg
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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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Mayer Goldberg. 2023-12-23. A Spigot-Algorithm for Square-Roots: Explained and Extended. https://arxiv.org/abs/2312.15338

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