The Babylonian method is very simple. Given a number n and a guess at its square root x, we make the observation that if x is an overestimate of the square root of n, then n / x will be an underestimate of the square root. In contrast, if x is an underestimate of the square root of n then n / x will be an overestimate (convince yourself of this with a bit of algebra). From this, it is reasonable to expect that the average of x and n / x is a better estimate of the square root than we started with. For this algorithm, your program should prompt the user for a number to take the square root of (you should allow floating point or integer values) and an initial guess, and apply the Babylonian method, printing out each estimate of the square root until the change in estimates is less than 1e-8.