Python program to calculate cube root of given number

Mathematically, the cube root of a particular number is defined as the value obtained when the number is divided by itself three consecutive times. It is the inverse operation of a cubic number. For example, the cube root of 216 is 6 because 6 × 6 × 6 = 216. The task of this article is to find the cube root of a given number using Python.

The cube root is represented using the symbol “$\mathrm{\sqrt[3]{a}}$”. The 3 in the symbol denotes that the value is divided thrice in order to achieve the cube root.

In Python, there are many ways to calculate the cube root of a number. Let's look at them one by one:

• Use a simple mathematical formula.

• Use the math.pow() function.

• Use the cbrt() function in numpy.

Input and output scenarios

Now let's look at some input and output scenarios to calculate the cube root of a given number -

Assuming that the given input number is positive, the output is displayed as −

Input: 8
Result: 2

Assuming that the given input is a negative number, the output is displayed as −

Input: -8
Result: -2

Assuming the input is a list of elements, the output is obtained by -

Input: [8, -125]
Result: [2, -5]

Use mathematical equations

Let’s start simple; we use a simple mathematical equation to find the cube root of a number in Python. Here, we find the $\mathrm{\frac{1}{3}}$ power of the input number.

Example 1: For positive numbers

The given is a Python program that calculates the cube root of a positive number.

#take an input number
num = 216

#calculate cube root
cube_root = num ** (1/3)

#display the output
print("Cube root of ", str(num), " is ", str(cube_root))

Output

The output of the above python code is −

Cube root of 216 is 5.999999999999999

Example 2: For negative numbers

Given the following Python program, calculate the cube root of a negative number.

#take an input number
num = -216

#calculate cube root
cube_root = -(-num) ** (1/3)

#display the output
print("Cube root of ", str(num), " is ", str(cube_root))

Output

Cube root of -216 is -5.999999999999999

Use math.pow() Function

math.pow(x, y) function returns the value of x raised to the power of y, where the value of x is always a positive number. So in this case, we use this function to raise the input number to its $\mathrm{\frac{1rd}{3}}$ power.

Example 1: For positive numbers

In the following Python program, we find the cube root of a positive input number

import math
#take an input number
num = 64

#calculate cube root
cube_root = math.pow(num, (1/3))

#display the output
print("Cube root of ", str(num), " is ", str(cube_root))

Output

The output of the implementation is −

Cube root of 64 is 3.9999999999999996

Example 2: For negative numbers

In the following Python program, we find the cube root of a negative input number.

import math
#take an input number
num = -64

#calculate cube root
cube_root = -math.pow(-num, (1/3))

#display the output
print("Cube root of ", str(num), " is ", str(cube_root))

Output

The output of the implementation is −

Cube root of -64 is -3.9999999999999996

Use numpy's cbrt() function

cbrt() is a built-in function in the numpy library that returns the cube root of each element in the input array. This method does not throw an error when calculating the cube root of a negative number, making it more efficient than the previous method.

Example

In the Python example below, we take the input using a Python list and find the cube root using the cbrt() function.

#import numpy library to access cbrt() function
import numpy as np

#take an input list
num = [64, -729]

#calculate cube root of each element in the list
cube_root = np.cbrt(num)

#display the output
print("Cube root of ", str(num), " is ", str(cube_root))

Output

When compiling and executing the above Python code, you can get the following output -

Cube root of [64, -729] is [ 4. -9.]

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