Square root of a number by newton's method in python

Asked by admin @ in Computers and Technology viewed by 307 People

Convert Newton’s method for approximating square roots in Project 1 to a recursive function named newton. (Hint: The estimate of the square root should be passed as a second argument to the function.) An example of the program

Answered by admin @


Answer:

import math


tolerance=0.00001

approximation=1.0


x = float(input("Enter a positive number: "))


def newton(number,approximation):


   approximation=(approximation+number/approximation)/2


   difference_value =abs(number-approximation**2)


   if difference_value<= tolerance:

       return approximation

   else:

       return newton(number,approximation)


print("The approximation of program = ", newton(x, approximation))


print("The approximation of Python = ", math.sqrt(x))

Explanation:    

  • Create a recursive function called newton that calls itself again and again to approximate square root for the newton technique.
  • Apply the formulas to find the estimate value  and the difference value
    .
  • Check whether the difference_value is less than the tolerance value  and then return the value of approximation  else make a recursive call to the newton function by passing the  user input and the new approximation value
    .
  • Finally display all the results using the print statement.

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