Python Square Root Without Math Module – ** or Newton’s Method

In Python, the easiest way to find the square root of a number without the math module is with the built in exponentiation operator **.

sqrt_of_10 = 10**(1/2)

When working with numeric data in Python, one calculation which is valuable is finding the square root of a number.

We can find the square root of a number easily with the math module, but sometimes we don’t want to import modules to our code.

We can also use the built in ** to find exponents in Python. To find a square root with the ** operator, we just put “(1/2)” after **.

Below are some examples of how to use the Python built in ** operator to find square roots.

import math

print(4**(1/2))
print(9**(1/2))
print(13**(1/2))
print(90**(1/2))
print(2182**(1/2))

#Output:
2.0
3.0
3.605551275463989
9.486832980505138
46.71188285650665

Finding the Square Root of a Number Without the Python math Module

We can also estimate the square root of a number without the Python math module. To compute the square root in Python without the Python math module, we can employ the help of Newton’s Method.

Newton’s method is a root finding algorithm which can help us find an approximation of a function.

We can use Newton’s method to find the square root of a number in Python.

Below is a function which you can use to utilize Newton’s method to find an approximation for the square root of a number to precision level “a”. For a comparison, we will also use the sqrt() function from the Python math module.

import math

def newton_sqrt(n,a):
    x = n
    while(True):
        root = 0.5*(x+(n/x))
        if (abs(root-x) < a):
            break
        x = root
    return root

print(math.sqrt(13))
print(newton_sqrt(13,0.1))

print(math.sqrt(50))
print(newton_sqrt(50,0.0001))

print(math.sqrt(100))
print(newton_sqrt(100,0.000001))

print(math.sqrt(313))
print(newton_sqrt(313,0.00000001))

#Output:
3.605551275463989
3.6063454894655185

7.071067811865477
7.0710678118654755

10.0
10.0

17.69180601295413
17.69180601295413

As shown above, Newton’s method allows us to get a pretty good approximation of the square root of a number without using the math module.

Hopefully this article has been beneficial for you to learn how to find the square root of a number without the math module in Python.