Question

Design an algorithm to find the square root of a positive number by starting with the number itself as the first guess and repeatedly producing a new guess from the previous one by averaging the previous guess with the result of dividing the original number by the previous guess. Analyse the control of this repetitive process. In particular, what condition should terminate the repetition?

Answer 1

I think this is the first video of those SICP lectures or somewhere in the SICP book :) nice

Answer 2

I made a quick console application in C# that does what You asked. Hope it helps:

double v = Convert.ToDouble(Console.ReadLine()); // the original number
double sqr = Math.Sqrt(v); // the square root of the number
double prevGuess = v; //the previous guess

while (prevGuess != sqr) // this loop iterates until the square root of the number is found
prevGuess = (prevGuess + (v / prevGuess)) / 2;

Console.Write(prevGuess); //write the result