The ancient Babylonians had an iterative technique for numerically approximating the values of square roots. Their method can be physically implemented using series and parallel resistor networks. A recursive formula for the equivalent resistance R[subscript eq] is developed and converted into a nonrecursive solution for circuits using geometrically increasing numbers of identical resistors. As an example, 24 resistors "R" are assembled into a second-order network and "R[subscript eq]/R" is measured to equal [image omitted] to better than 0.2%, as could be done in an introductory physics laboratory. (Contains 1 table and 5 figures.)