Question

Package Newton’s method for approximating square roots (Case Study 3.6) in a function named newton. This function expects the input number as an argument and returns the estimate of its square root. The script should also include a main function that allows the user to compute square roots of inputs until she presses the enter/return key.

Answer 1

The newton function can be implemented in Python using Newton's method for approximating square roots. The main function can then call the newton function repeatedly until the user presses the enter/return key.

Step-by-step explanation:

The newton function can be implemented in Python using Newton's method for approximating square roots. Here's how you can define the newton function:

def newton(number):
guess = number / 2
while True:
new_guess = (guess + number / guess) / 2
if abs(guess - new_guess) < 0.0001:
return new_guess
guess = new_guess
The main function can then call the newton function repeatedly until the user presses the enter/return key:def main():
while True:
user_input = input('Enter a number (or press enter to quit): ')
if user_input == '':
break
number = float(user_input)
square_root = newton(number)
print('Square root of', number, 'is', square_root)

main()

Answer 2

The question is about creating a programming function named newton that utilizes Newton's method for an efficient approximation of square roots without solving for quadratic equation roots. The function is applicable in various mathematical scenarios, particularly where manual computation is required, such as in equilibrium problems.

Step-by-step explanation:

The student's question relates to the programming of a function called newton that implements Newton's method for approximating square roots. The method is a mathematical approach that allows for expedient calculations by avoiding the need to solve for the roots of a quadratic equation. Newton's method is particularly useful in situations where square roots need to be computed manually or understood conceptually, such as in some equilibrium problems in chemistry or physics. By creating a function and utilizing a loop, users can repeatedly input numbers and receive an estimate of the square root until the enter/return key is pressed.

In the context of programming, it can be wrapped in a function to allow for repeated efficient calculation of the square root of any positive number. The square root function is fundamental in handling various mathematical computations like in equilibrium problems or any scenario where roots need to be analyzed for a final answer. Also, understanding the approximate square root computation is beneficial for students working without a calculator or aiming to grasp the underpinning principles of square roots and exponents, as indicated by √x² = √x.