Square Root in Python

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While working with mathematical operations in Python, one of my team members was required to calculate the square root of a number in Python. I thought of writing a complete tutorial. In this tutorial, I will discuss everything about square root in Python with examples.

To calculate the square root in Python, you can use the math.sqrt() function from the built-in math module. First, import the module using import math, then call math.sqrt(x) where x is the non-negative number you want the square root of. For example, math.sqrt(25) will return 5.0.

What is a Square Root in Python?

A square root of a number ( x ) is a number ( y ) such that ( y^2 = x ). In other words, it is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because ( 4 \times 4 = 16 ).

There are multiple ways to find the sqrt of a number in Python:

Using math.sqrt() function
Using exponentiation operator

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Python math.sqrt() Function

Python provides a built-in module called math that includes a function for calculating the square root. The math.sqrt() function is the most efficient method for finding the square root in Python.

Syntax

Here is the syntax of the sqrt() function in Python.

import math result = math.sqrt(x)

The math.sqrt() function takes a single argument x and returns the square root of x. The argument must be a non-negative number; otherwise, it will raise a ValueError.

Example

Now, let me show you an example of finding the sqrt of a number in Python.

Let’s calculate the square root of 25; you can use the below Python code.

import math number = 25 result = math.sqrt(number) print(f"The square root of {number} is {result}")

Output:

The square root of 25 is 5.0

I executed the above Python code using VS code and you can see the output in the screenshot below:

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Using Exponentiation Operator

Another way to calculate the square root in Python is by using the exponentiation operator **. This method is also simple and effective.

Syntax

Here is the syntax:

result = x ** 0.5

By raising a number to the power of 0.5, you can obtain its square root. This method can be particularly useful for quick calculations without importing any modules.

Example

Now, let me show you an example.

Let’s calculate the square root of 49:

number = 49 result = number ** 0.5 print(f"The square root of {number} is {result}")

Output:

The square root of 49 is 7.0

Here is the output in the screenshot below:

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Handle Complex Numbers

When dealing with negative numbers, the square root calculation results in a complex number. Python’s cmath module can handle these cases.

Syntax

Here is the syntax:

import cmath result = cmath.sqrt(x)

The cmath.sqrt() function returns the square root of a number, including complex results for negative inputs.

Example

Now, let me show you an example.

Let’s calculate the square root of -16:

import cmath number = -16 result = cmath.sqrt(number) print(f"The square root of {number} is {result}")

Output:

The square root of -16 is 4j

Here is the exact output in the screenshot below:

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Square Root in Python – Examples

Now, let me show you two real examples of finding square root in Python.

Real Estate Scenario

Imagine you’re a real estate developer in New York, and you need to calculate the side length of a square plot given its area. Then, you can write the Python code below.

import math area = 10000 # in square feet side_length = math.sqrt(area) print(f"The side length of a square plot with an area of {area} sq ft is {side_length} ft")

Output:

The side length of a square plot with an area of 10000 sq ft is 100.0 ft

Here is the exact output in the screenshot below:

Finance Scenario

Suppose you’re a financial analyst in San Francisco and need to calculate a stock’s volatility given its variance. Here is the complete Python code.

import math variance = 0.04 volatility = math.sqrt(variance) print(f"The volatility of the stock is {volatility}")

Output:

The volatility of the stock is 0.2

Conclusion

In this tutorial, I explained how to calculate the square root in Python using different methods, such as the math.sqrt() function, the exponentiation operator, or handling complex numbers with cmath, etc. I have also provided two different real examples related to square root in Python.

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