Question

Package Newton’s 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 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

Answer:

def newton(n):

       #Define the variables.

       t = 0.000001

       esti = 1.0

       #Calculate the square root

       #using newton method.

       while True:

               esti = (esti + n / esti) / 2

               dif = abs(n - esti ** 2)

               if dif <= t:

                       break

   

       #Return the result.

       return esti

#Define the main function.

def main():

   

       #Continue until user press enters.

       while True:

               try:

         

                       #Prompt the user for input.

                       n = int(input("Enter a number (Press Enter to stop):"))

                       #display the results.

                       print("newton = %0.15f" % newton(n))

     

               except:

                       return

#Call the main function.

main()