The ancient Greeks knew how to efficiently compute square roots. If you want the square root of a and already have a guess x_old for it, then you can have a better guess as the average of x_old and a / x_old, i.e.

x_new = (x_old + a / x_old) / 2

For the initial guess, set x_old to a.

Implement a program that reads a, prompting the user until a positive number is entered, and that prints all guesses other than the initial one, until two of them are less than 10^-12 apart.

Print the guess number in a field of width 2 and the guess in a field of width 20 with twelve digits after the decimal separator.