Restructure Newton's method (Case Study: Approximating Square Roots) by decomposing it into three cooperating functions.

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 function named limitReached, whereas the task of computing a new approximation is assigned to a function named improveEstimate. Each function expects the relevant arguments and returns an appropriate value.

The code that needs modified is below:

# Modify the code below

"""

Program: newton.py

Author: Ken

Compute the square root of a number.

1. The input is a number.

2. The outputs are the program's estimate of the square root

using Newton's method of successive approximations, and

Python's own estimate using math.sqrt.

"""

import math

# Receive the input number from the user

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

# Initialize the tolerance and estimate

tolerance = 0.000001

estimate = 1.0

# Perform the successive approximations

while True:

estimate = (estimate + x / estimate) / 2

difference = abs(x - estimate ** 2)

if difference <= tolerance:

break

# Output the result

print("The program's estimate is", estimate)

print("Python's estimate is ", math.sqrt(x))