You can estimate the square root of a number n by iterating the expression (1/2)(n+2/n). That is, you get the first estimate by n1 = (1/2)(n+2/n), then the second, better, estimate by n2 = (1/2)(n1+2/n1), then the third estimate by n3 = (1/2)(n2+2/n2) and so on. However, you will probably still need a calculator to do these calculations!!