Square Root Calculator Python with Math

How to Calculate Square Roots in Python

Calculating square roots in Python is straightforward using the built-in math module. The square root of a number is the value that, when multiplied by itself, gives the original number.

For real numbers, use math.sqrt(). For complex numbers, use cmath.sqrt(). Here's how to implement both:

Python Square Root Code Examples

import math
import cmath

# Real number square root
real_num = 16
real_sqrt = math.sqrt(real_num)
print(f"Square root of {real_num} is {real_sqrt}")

# Complex number square root
complex_num = -16
complex_sqrt = cmath.sqrt(complex_num)
print(f"Square root of {complex_num} is {complex_sqrt}")

The math.sqrt() function returns a float, while cmath.sqrt() returns a complex number. Both functions raise a ValueError if given a negative number to math.sqrt().

Square Root Formula

The square root of a number \( x \) is a value \( y \) such that:

Square Root Formula

\( y = \sqrt{x} \) where \( y^2 = x \)

For real numbers, \( x \) must be non-negative. For complex numbers, the formula extends to:

Complex Square Root Formula

\( \sqrt{x} = \pm \sqrt{\frac{|x|}{2}} \pm i \sqrt{\frac{|x|}{2}} \)

Where \( i \) is the imaginary unit (\( i^2 = -1 \)).

Worked Examples

Example 1: Real Number Square Root

Calculate the square root of 25:

Using Python:

import math
print(math.sqrt(25))  # Output: 5.0

Example 2: Complex Number Square Root

Calculate the square root of -9:

Using Python:

import cmath
print(cmath.sqrt(-9))  # Output: 3j

This returns \( 3i \) because \( (3i)^2 = -9 \).

Frequently Asked Questions

What is the difference between math.sqrt() and cmath.sqrt()?: math.sqrt() works only with real numbers and returns a float. cmath.sqrt() works with complex numbers and returns a complex number.
Can I calculate the square root of a negative number with math.sqrt()?: No, math.sqrt() raises a ValueError for negative numbers. Use cmath.sqrt() instead.
How accurate are Python's square root calculations?: Python uses IEEE 754 double-precision floating-point arithmetic, which provides about 15-17 significant decimal digits of precision.
Can I calculate the square root of a matrix in Python?: Yes, you can use libraries like NumPy's numpy.linalg.sqrtm() function for matrix square roots.