Perfect Solution Ramesh, Just iterating more with example -
Cube root of a number a is obtained by starting with a guess x1 of the cube root and using the formula
x2 = (1/3)[2 x1 + a/(x1^2)]
So say to find the cube root of 5, we take x1 as 3/2. (This guess is based on the reasoning that a value of 2 will be too high since the cube of 2 is 8 wheres as a value of 1 is too low since the cube of 1 is 1)
So x2 = (1/3)(2(3/2) + 5/(9/4)) = 1 + 20/27 = 47/27. We then let x1 = 47/27 and repeat the process, successively finding better and better approximations to the cube root of 5.