Package Newtons method for approximating square roots (Case Study: Approximating Square Roots) in a function named newton. This function expects the input number as an argument and returns the estimate of its square root. The program should also include a main function that allows the user to compute the square roots of inputs from the user and python's estimate of its square roots until the enter/return key is pressed.

An example of the program input and output is shown below:

Enter a positive number or enter/return to quit: 2

The program's estimate is 1.4142135623746899

Python's estimate is 1.4142135623730951

Enter a positive number or enter/return to quit: 4

The program's estimate is 2.0000000929222947

Python's estimate is 2.0

Enter a positive number or enter/return to quit: 9

The program's estimate is 3.000000001396984

Python's estimate is 3.0

Enter a positive number or enter/return to quit

# Modify the code below to have the above output:

"""

File: newton.py

Project 6.1

Compute the square root of a number (uses function with loop).

1. The input is a number, or enter/return to halt the

input process.

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.

"""

#Define the function newton()

#This function expects the input number as an argument

#returns the estimate of its square root

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))