from math import sqrt

def newton(num, guess):
    # Constant that says how close our answer has to be to right.
    epsilon = 0.00001
    # Initialize next to the initial guess
    next = guess

    # Keep looping until next^2 gets close to num.
    while abs((next*next) - num) > epsilon:
        # This is Newton's suggestion for what value to try next.
        next = (next + num/next)/2
    return next

def main():
    print("Welcome to the Newton's Method program.")

    number = int(input("What number do you want the root of? "))
    guess = int(input("What is your initial guess? "))

    # Get the answer from our newton function
    root = newton(number, guess)

    # Calculate the actual root using Python's sqrt function
    realroot = sqrt(number)

    # Print the results.
    print("Newtons root: ", root, " Real root: ", realroot)

    print("Difference is: ", abs(root-realroot))