Instructions newton.py + 1 # Modify the code below 2 Restructure Newton's method (Case Study: Approximating Square Roots) by decomposing it into 3 Program: newton.py three cooperating functions: newton, limitReached , and improveEstimate. 4 Author: Ken 5 Compute the square root of a number. 6 1. The input is a number. 7 2. The outputs are the program's estimate of the square root using Newton's method of successive approximations, and The newton function can use either the recursive strategy of Project 2 or the iterative strategy of the Approximating Square Roots Case Study. The task of testing for the limit is assigned to a 8 function named limitReached, whereas the task of computing a new approximation is assigned 9 Python's own estimate using math.sqrt. to a function named improveEstimate.Each function expects the relevant arguments and 10 "H 11 returns an appropriate value. 12 import math 13 An example of the program input and output is shown below: 14 # Receive the input number from the user 15 x = float(input("Enter a positive number: ")) 16 Enter a positive number or enter/return to quit: 2 17 # Initialize the tolerance and estimate 18 tolerance = 0.000001 The program's estimate is 1.4142135623746899 19 estimate = 1.0 20 Python's estimate is 1.4142135623730951 Enter a positive number or enter/return to quit 21 # Perform the successive approximations 22 while True: estimate = (estimate + x / estimate) / 2 difference = abs(x - estimate ** 2) if difference <= tolerance: 23 24 25 26 27 28 # Output the result 29 print("The program's estimate is", estimate) 30 print("Python's estimate is 31 break ", math.sqrt(×))