math.sqrt() returns the square root of a number. It is an inbuilt function in the Python programming language, provided by the math module. In this article, we will learn about how to find the square root using this function.

Example:

import math 

# square root of  0 
print(math.sqrt(0)) 

# square root of 4
print(math.sqrt(4)) 

# square root of 3.5
print(math.sqrt(3.5))

0.0
2.0
1.8708286933869707

We need to import math before using this function.

import math

math.sqrt() syntax

math.sqrt(x)

Parameter:

• x: A number greater than or equal to 0.

Returns:

• The square root of the number x.

math.sqrt() examples

Let's look at some different uses of math.sqrt() .

Example 1: Check if number is prime

math.sqrt() can be used to optimize prime number checking. We only need to check divisibility up to the square root of the number.

import math

n = 23 # Check if 23 is prime

# Check if n is equal to 1
if n == 1:
    print("not prime")
else:
    
    # Loop from 2 to the square root of n 
    for x in range(2, int(math.sqrt(n)) + 1):
        if n % x == 0:
            print("not prime")
            break  # Exit the loop
    else:
        print("prime")

prime

Explanation

• If n > 1, we check for factors from 2 to sqrt(n).
• If any divisor is found, it prints "Not prime".
• If no divisors are found, it prints "Prime".

Example 2: Finding hypotenuse of a triangle

We can use math.sqrt() to find the hypotenuse of a right-angled triangle using the Pythagorean theorem.

a = 10
b = 23
import math

c = math.sqrt(a ** 2 + b ** 2)
print(c)

The value for the hypotenuse would be  25.079872407968907

Explanation

• The formula used is c = sqrt(a^2 + b^2).
• It calculates the hypotenuse c using the values of a and b.

Error handling

math.sqrt() does not work for negative numbers. It raises a ValueError if we pass a number less than 0.

import math

# error when x<0
print(math.sqrt(-1))

Output

Traceback (most recent call last):
  File "/home/67438f8df14f0e41df1b55c6c21499ef.py", line 8, in 
    print(math.sqrt(-1)) 
ValueError: math domain error

Explanation

• Square roots of negative numbers are not real numbers.
• math.sqrt() only works with non-negative values.