  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.
