Python Find Square Root of a Number

The square root of a number x is a value y such that when y is multiplied by itself, it equals x.

• Mathematical Representation: √x = y where y × y = x
• For Example: √25 = 5 because 5 × 5 = 25

Python has several methods to find the square root of a number. Here are a few common approaches, each with an explanation and example.

Each method has its use case, depending on whether you’re working with simple numbers, complex numbers, or more advanced mathematical operations.

1. Using the Exponentiation Operator (**)

The ** operator in Python is the exponentiation operator, used to raise a number to a power (e.g., a ** b computes a^b). This is the simplest method in Python for calculating the square root of a given number. The square root of a number is equivalent to raising the number to the power of 0.5.

Code Example

num = float(input("Enter a number: "))
sqrt = num ** 0.5
print(f"The square root of {num} is {sqrt}")Code language: Python (python)

Output

# Enter a number: 0
# The square root of 0.0 is 0.0

# Enter a number: 64
# The square root of 64.0 is 8.0

# Enter a number: 3.5
# The square root of 3.5 is 1.8708286933869707

# Enter a number: -64
# The square root of -64.0 is (4.898587196589413e-16+8j)

Explanation

• Here, we are taking the number as input from the user. And converting it to the float.
• The expression num ** 0.5 calculates the square root by raising the number to the power of 0.5.
• Note: This calculation does not work for negative numbers. In case of a negative number, it gives an invalid answer.

2. Using math.sqrt() Function

math.sqrt() is a function in Python’s math module that returns the square root of a given non-negative number. This method is helpful because it’s a dedicated function for this operation and ensures precision.

Syntax – math.sqrt(x)

• It takes one argument (a number) and returns the square root.
• x must be non-negative (x ≥ 0).
• Returns a floating-point value.
• Raises a ValueError if x is negative.

Code Example

import math

print('square root of 0: ', math.sqrt(0))
print('square root of integer number 64: ', math.sqrt(64))
print('square root of float number 5.6: ', math.sqrt(5.6))Code language: Python (python)

Output

square root of 0:  0.0
square root of integer number 4:  8.0
square root of float number 5.6:  2.3664319132398464

3: Using cmath.sqrt() Function for complex numbers

To calculate the square root of a number in Python the cmath module can be used when dealing with both real and complex numbers. It is useful for finding square roots of negative numbers.

Code Example

import cmath

print('square root of integer number 64: ', cmath.sqrt(64))
print('square root of float number 5.6: ', cmath.sqrt(5.6))
print('square root of negative number -64: ', cmath.sqrt(-64))Code language: Python (python)

Output:

square root of integer number 64:  (8+0j)
square root of float number 5.6:  (2.3664319132398464+0j)
square root of negative number -64:  8j

Explanation

• cmath.sqrt() can handle both real and complex numbers.
• If the input is negative, this function returns a complex number as the square root.
• For example, cmath.sqrt(-144) returns 12j and cmath.sqrt(144) returns 12+0j
• In Python, 12+0j and 12j are both complex numbers, but they represent different values.
  • 12+0j: This is a complex number with a real part of 12 and an imaginary part of 0.
  • 12j: This is a purely imaginary number with no real part and an imaginary part of 12.