I would think that rather than guessing between decimal multiples of 2 and 7, you would extract the even powers of 10 and then look for the square root of numbers between 1 and 100, (or extract all powers of ten, and if its odd (say 2n+1), you calculate the square root of a number between 1 and 10 and then multiply it by tabulated value of sqrt(10)* 10^n. Anyways, this was just a thought. One can probably improve the babylonian method in a variety of ways.