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.

翻译：本文介绍并扩展了一种用于逐位计算平方根的已知数字提取算法，该算法仅需加法和减法，适合手算或算盘操作。我们给出了原始算法正确性的初等证明，随后提出了相应的立方根数字提取算法。最后，我们将该算法推广至求解r次方根，并展示了如何针对任意r优化该算法。所得到的算法仅需要整数加法和减法。