The function sqrt from the header file cmath can be used to find the square root

Question

The function sqrt from the header file cmath can be used to find the square root of a nonnegative real number. Using Newton’s method, you can also write an algorithm to find the square root of a nonnegative real number within a given tolerance as follows: Suppose x is a nonnegative real number, a is the approximate square root of x, and epsilon is the tolerance. Start with a = x.

If |a2– x| <= epsilon, then a is the square root of x within the tolerance, otherwise:

Replace a with (a2 + x) / (2a) and repeat Step a in which |a2– x| denotes the absolute value of a2– x.

Write a recursive function to implement this algorithm to find the square root of a nonnegative real number. Also, write a program to test your function.

Explanation / Answer

solution--

save the file as test.py and run it from command line as python test.py

x=100 # input number
a=x
eps=1 # you can change the error
while (a**2-x)>eps:
   a=(a**2+x)/(2*a)
print(a)

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