Find Square root using Babylonian method(Efficient)

Perhaps the first algorithm used for approximating  is known as the "Babylonian method", named after the Babylonians, or "Heron's method", named after the first-century Greek mathematician Hero of Alexandria who gave the first explicit description of the method. It can be derived from (but predates) Newton's method. This is a quadratically convergentalgorithm, which means that the number of correct digits of the approximation roughly doubles with each iteration. It proceeds as follows:

1. Begin with an arbitrary positive starting value x₀ (the closer to the root, the better).
2. Let x_n+1 be the average of x_n and S / x_n (using thearithmetic mean to approximate the geometric mean).
3. Repeat step 2 until the desired accuracy is achieved.

It can also be represented as:

This algorithm works equally well in the p-adic numbers, but cannot be used to identify real square roots with p-adic square roots; it is easy, for example, to construct a sequence of rational numbers by this method that converges to + 3 in the reals, but to − 3 in the 2-adics.

Java Code :

public static double getSquareRoot(double s) {
  double Xn = 2.0;
  double lastXn = 0.0;
  while (Xn != lastXn) {
   lastXn = Xn;
   Xn = (Xn + s / Xn) / 2.0;
  }
  return Xn;
 }

 Refer : http://www.ardendertat.com/2012/01/26/programming-interview-questions-27-squareroot-of-a-number/