How to Compute Square Roots in Python

A high-level, multi-paradigm programming language with an object-oriented approach, Python is designed to be highly extensible, with multiple compact modules, including a multi-functional math module. 

Here, we explore the different ways in which Square Roots in Python can calculate a very specific mathematical functionality – square roots – with or without the use of its math and cmath modules.

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What is a Square Root?

While most of us are familiar with this mathematical concept, it’s worth refreshing our memory with a simple definition: The value ‘y’ is x’s square root because ‘y’, when multiplied by itself, yields the original number x.
In mathematical terms this may be expressed as follows:
If x = y x y
or x = y2
then √x = y

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Square Root Function in Python

A number’s square root may be extricated using Python in a variety of different ways. The most commonly used square root function in Python is math.sqrt(), which provides an efficient way to compute the square root of a given number. 

However, Python also allows alternative approaches, such as:

1. Using the Python math module:

A. With the inbuilt math.sqrt( ) function:
Step 1: Import the math module
Step 2: Use the sqrt( ) function
Input code:
Import math
Print(“54’s square root is” ,math.sqrt(49))
Output:
54’s square root is 7.348469228349534
B. With the inbuilt math.pow( ) function:
Step 1: Import the math module
Step 2: Use the pow( ) function
This operates on the simple mathematical principle: √x = x1/2  or  √x = x0.5.
The function requires the input of two parameters – the base number and its exponent.
Input code:
Import math
number = float(input(” Please Enter any numeric Value : “))
squareRoot = math.pow(number, 0.5)
print(“The given number {0}’s square root = {1}”.format(number, squareRoot))
Output:
Please Enter any numeric Value: 54
The Given Number 54.0’s square root = 7.348469228349534

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2. Using the Python cmath module

Step 1: Import the complex math (cmath) module
Step 2: Use the cmath.sqrt( ) function
The cmath module helps compute the  square root of real or complex numbers.
Input code:
import cmath
num = 1+2j
sqrt = cmath.sqrt(num)
print(‘{0}’s square root is {1:0.2f} + {2:0.2f}’ .format(num,sqrt.real,sqrt.imag))
Output:
(1+2j)’s square root is 1.27+0.79

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3. Using the exponent ** operator:

Operates on the same principle as the pow( ) function, i.e. √x = x1/2  or  √x = x0.5
but does not require users to import the math module
Input code:
def sqrt(n):
if n < 0:
Return
Else:
return n**0.5
print(sqrt(54))
Output:
7.348469228349534

By using the sqrt in Python, you can efficiently compute square roots with built-in functions and mathematical principles

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Conclusion

Computing the square root in Python is simple and can be done using various methods. The most common approach is using the math.sqrt() function, while the exponentiation operator (**0.5) provides an alternative without importing modules. 

For working with arrays, numpy.sqrt() is efficient, and if dealing with negative numbers, cmath.sqrt() handles complex roots. Additionally, custom algorithms like the Newton-Raphson method can be used for iterative approximations.

By understanding these different techniques, you can efficiently compute the square root in Python based on your specific use case.