#Babylonian Method
The iterative method for finding square roots is called the Babylonian method.
#Algorithm
1)Start with an arbitrary positive start value x (the closer to the root, the better). 2)Initialize y = 1. 3) Do following until desired approximation is achieved. a) Get the next approximation for root using average of x and y b) Set y = n/x
#Example
n = 4 /n itself is used for initial approximation/ Initialize x = 4, y = 1 Next Approximation x = (x + y)/2 (= 2.500000), y = n/x (=1.600000) Next Approximation x = 2.050000, y = 1.951220 Next Approximation x = 2.000610, y = 1.999390 Next Approximation x = 2.000000, y = 2.000000 Terminate as (x - y) > e now.