Python sqrt

The Python sqrt() function is a built-in math library function used to find the square root of a specified expression or a specific number. Finding the square root is crucial in solving mathematical equations, scientific calculations, and so on.

In Python, there are multiple approaches to calculating the square root, including math.sqrt(), the exponent operator, NumPy module, cmath, and other approaches. In this article, we show how to use the Python sqrt() function in detail, with syntax and real-time examples.

Example

import math
print(math.sqrt(100))
10.0

Python sqrt() syntax

The syntax of this math function is:

math.sqrt(number);

The argument can be a number or a valid numerical expression. If the number argument is a positive integer, the math.sqrt function returns the square root of a given value.

  • If the parameter value is 0, it returns 0.0 as output.
  • If the given number is a negative integer, it returns ValueError.
  • And if it is not a number, the sqrt() returns TypeError.

Return Value: The Python sqrt() function calculates the square root of a number, and always returns a floating-point number as output.

NOTE: To use the sqrt() function, we must import the math module (import math).

Python sqrt() function examples

Using math.sqrt() function on positive numbers

In the example below, we declared a variable and assigned 36 to it. Next, we used the built-in math.sqrt() function to find the square root of a perfect square number. To display the result type, we used an extra print statement to show the return type (float).

import math
n = 36
res = math.sqrt(n)
print(res)
print(type(res))
6.0
<class 'float'>

Finding the square root of a Zero

In the following example, we pass parameter 0 to the sqrt() function to find the square root of zero.

import math
print(math.sqrt(0))
0.0

Using the Python sqrt() function with floating-point numbers

The sqrt() function also allows the use of a floating-point number (with decimals) as a parameter. The following example uses the sqrt() to find the square root of a floating-point number.

import math
n = 16.5
print(math.sqrt(n))
4.06201920231798

To find the accuracy of the produced result, use the ** operator.

print(4.06201920231798 ** 2)
16.500000000000004

Python sqrt() function handling negative numbers

The built-in sqrt() function accepts only positive numbers. If you try to find the square root of negative numbers, the sqrt() function returns a ValueError.

In the following example, we declared a variable and assigned -16 as its value. Next, used the math.sqrt() on it.

import math
n = -16
print(math.sqrt(n))
Traceback (most recent call last):
  File "C:\....\.....\.....\.....\example.py", line 3, in <module>
    print(math.sqrt(n))
          ~~~~~~~~~^^^
ValueError: math domain error

To handle this error, we have two options.

Checking if the number is greater than 0

We can use the if statement to check whether the given number is greater than or equal to 0. If true, apply the math.sqrt() function. Otherwise, print a message.

import math
n = -16
if n >= 0:
    res = math.sqrt(n)
    print(res)
else:
    print("Positive Numbers only")
Positive Numbers only

TIP: If you change n value to 16, it returns 4.0.

Using try and except in Python sqrt function

When working with user inputs or a large dataset, it is best to use try and except to catch those ValueError.

import math
n = -16
try:
    res = math.sqrt(n)
    print(res)
except ValueError:
    print("Invalid input")
Invalid input

Using the Python sqrt() function on a string

When you use the math sqrt() function on a string data type, it will throw a TypeError. However, if your data is numeric, we can convert the string to a floating-point number and apply the sqrt function.

For instance, the code below throws an error because n is a string data type.

import math
n = "25"
print(math.sqrt(n))
TypeError: must be real number, not str

Let me use the float() function to convert the string to a floating-point number and apply the sqrt() function.

import math
n = "25"
print(math.sqrt(float(n)))
5.0

Using the cmath module

There is a Python sqrt() function in the cmath module that supports negative numbers as a parameter and finds the square root. However, the cmath.sqrt() returns a complex number.

import cmath
n = -25
print(cmath.sqrt(n))
5j

We can also use the cmath module’s sqrt() function to find the square root of a complex number.

import cmath
x = 3 + 4j
print(cmath.sqrt(x))
(2+1j)

math.isqrt() function – Integer Square root

As we mentioned earlier, the Python sqrt() function returns a floating-point number. However, the math module has the isqrt() function, which calculates the square root of a given number and returns the integer as output.

NOTE: If you pass a floating-point number as the argument, the isqrt() method returns TypeError.

import math
print(math.isqrt(25))
5

The above example is a perfect square. However, if you pass a non-perfect square number, the round will be the largest integer value less than or equal to the result. For example, if you pass any number between 25 and 35, the isqrt() method returns 5. If you pass 36, it returns 6, and that 6 number continues up to the parameter value of 49.

Using the exponentiation operator

If you don’t want to use the built-in sqrt() function, the exponentiation operator is the simplest way to calculate the square root of a number. This operator, denoted by **, allows one to raise a given number to a specific power. If we set the power to 0.5, it returns the square root.

n = 49
print(n ** 0.5)
7.0

Python sqrt function on list and tuple

In all the above mentioned examples, we use the sqrt() function to calculate the square root of a single value. However, we can use it on the list or tuple items.

In this example, we will calculate the square root of different data types, including list items, tuple items, string data type, and numeric expressions, and display the output.

  1. Within the first two statements, we used both positive integers to calculate the Python square root.
  2. Next two statements, we used it on Tuple and List items. If you observe the following screenshot, this math method is working for them perfectly.
  3. Next statement, we tried the math sqrt function directly on multiple values (expression) to find the square root.
  4. Next, we tried on the string value, and it returned TypeError as output.
Python sqrt math function Example

List Comprehension

In the previous example, we used the index position to find the square root of a single list or tuple item. Here, we use the for loop or list comprehension to apply sqrt() on all list and tuple items to calculate the square root.

import math

n = [4, 9, 16, 25, 36, 49, 64, 81, 100]
s = [math.sqrt(i) for i in n]
print(s)
[2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]

Using a for loop

To trim the extra decimal points, we used the round() function. Here, the for loop iterates over the list items, and the Python sqrt() function calculates the square root of each number. The append() adds items to a new list.

import math

n = [4, 9, 16, 25, 36, 49, 64, 81, 100]
s = []
for i in n:
    s.append(round(math.sqrt(i)))

print(s)
[2, 3, 4, 5, 6, 7, 8, 9, 10]

Using Python numpy sqrt() function

The NumPy module has a built-in sqrt() function, which we can use to calculate the square root of an array, list, or large dataset. If there is already a dataset, using a for loop or list comprehension to iterate over each list item is not a viable option. Instead, convert the existing list to a numpy array and apply the sqrt() function on the complete array

import numpy as np

n = np.array([25, 36, 49, 64])
s = np.sqrt(n)
print(s)
[5. 6. 7. 8.]

NumPy sqrt() function on a multidimensional array

The numpy module’s sqrt() function is not limited to a single array; we can use it on multidimensional arrays (matrices) of any size and shape.

import numpy as np

n = np.array([[25, 36, 49], [64, 81, 100]])
s = np.sqrt(n)
print(s)
[[ 5.  6.  7.]
[ 8.  9. 10.]]

Python sqrt() function: Real-time examples

Use math.sqrt() function to find the distance between two points

The mathematical formula to find the distance between the two points is

X = √((x2 – x1)2 + (y2 – y1)2)

To demonstrate it, we will find the distance between (3, 2) and (9, 7) coordinate points. Here, the final output is the square root of 61, which equals 7.81.

import math
x = (3, 2)
y = (9, 7)
distance = math.sqrt((y[0] - x[0])**2 + (y[1] - x[1])**2)
print(distance)
7.810249675906654

Pythagoras Theorem -Diagonal distance

If we know the length of the two sides of a right-angled triangle, we can use Pythagoras’ theorem to calculate the length of the hypotenuse.

import math
a = 6
b = 10
hypotenuse = math.sqrt(a**2 + a**2)
print(hypotenuse)
8.48528137423857

TypeError: Complex Numbers

When we pass a complex number to the math.sqrt() function, it returns a TypeError.

import math
z = 10 + 12j
print(math.sqrt(z))
TypeError: must be real number, not a complex

TIP: Use the cmath sqrt() function to deal with complex numbers.

Implementing the Newton-Raphson method

Please refer to functions, while loop, and abs() function.

def newton_raphson(n, tolerance=1e-10):
    i = n / 2

    while abs(i * i - n) > tolerance:
        i = (i + n / i) / 2

    return round(i, 2)

print(newton_raphson(36))
print(newton_raphson(5))
6.0
2.24

Difference between sqrt and Exponent Operator

Although the exponent operator does not require importing the math library, it is always advisable to use the math.sqrt() function.

Difference between math.sqrt and numpy.sqrt()

If you are working with arrays, data science, or large data, use numpy.sqrt() function. For single values and basic numerical calculations, use the math.sqrt() function.