# Find NTH Root of X Value in Python

Abdul Jabbar Oct 10, 2023

The nth root of a number x refers to finding a value y that, when raised to the power of n, results in x. In mathematical terms, for a given positive integer n, the nth root of x is denoted as `y = x^(1/n)`.

Understanding and calculating nth roots are fundamental concepts in mathematics, engineering, computer science, and various scientific disciplines. It’s essential for solving equations, analyzing data, and conducting a wide range of computations.

Python, being a versatile programming language, provides several methods and libraries to efficiently calculate the nth root of a given value x. The cube root (3rd root) of x can easily be found using the `numpy.cbrt()` function, and similarly, the square root (2nd root) of (x) can easily be determined using the `numpy.sqrt()` built-in function.

In this article, we will explore the methods to calculate the nth root of x in Python using the exponentiation operator, the `math` module, and the `numpy` library.

## Find the NTH Root of X Value in Python Using NumPy `power()`

NumPy is a powerful library in Python for numerical computing. The `power()` function in NumPy is used to raise the elements of an array to a specified power, but it can also be used for a single value.

The syntax is as follows:

``````result = np.power(base, exponent)
``````

Here, `base` is the number you want to raise to a power, and `exponent` is the power to which you want to raise the base.

To find the nth root of a number x, we can use the `power()` function from NumPy by raising x to the power of (1 / n). The formula for finding the nth root is as follows:

``````nth_root = np.power(x, 1 / n)
``````

Here, `x` is the value for which we want to find the nth root, and `n` is the degree of the root.

Let’s illustrate this with an example:

``````import numpy as np

def find_nth_root(x, n):
nth_root = np.power(x, 1 / n)
return nth_root

x = 16
n = 4

result = find_nth_root(x, n)
print(f"The {n}th root of {x} is: {result}")
``````

Output:

``````The 4th root of 16 is: 2.0
``````

Here, we begin by importing the NumPy library using `import numpy as np`. Next, we defined a function `find_nth_root`, which takes two arguments: `x` representing the number for which we want to find the nth root, and `n` indicating the degree of the root we seek.

Within the function, we used the NumPy `power()` function, taking `x` and `1 / n` as arguments. This calculates the nth root of `x` by raising `x` to the power of `1 / n`.

The result is assigned to the `nth_root` variable and then returned.

For the example usage, `x` is assigned the value 16, representing the number for which we want to calculate the nth root. `n` is set to 4, indicating that we’re aiming to find the 4th root of 16.

The `find_nth_root` function is invoked with these parameters, and the calculated nth root is stored in the variable `result`.

Lastly, we used a formatted string to present the result.

## Find the NTH Root of X Value in Python Using the Power Operator

The power operator in Python is denoted by `**`. It raises a number to a specified power.

The syntax is as follows:

``````result = base ** exponent
``````

Here, `base` is the number you want to raise to a power, and `exponent` is the power to which you want to raise the base.

To find the nth root of a number x, we can use the power operator by raising x to the power of (1 / n). The formula for finding the nth root is as follows:

``````nth_root = x ** (1 / n)
``````

Here, `x` is the value for which we want to find the nth root, and `n` is the degree of the root.

Let’s illustrate this with an example:

``````def find_nth_root(x, n):
nth_root = x ** (1 / n)
return nth_root

x = 16
n = 4

result = find_nth_root(x, n)
print(f"The {n}th root of {x} is: {result}")
``````

Output:

``````The 4th root of 16 is: 2.0
``````

The provided code defines a Python function `find_nth_root(x, n)` that calculates the nth root of a given number `x` using the power operator. Inside the function, the nth root is computed by raising `x` to the power of `1/n`, effectively finding the nth root.

The code demonstrates an example usage, where `x` is set to 16 and `n` is set to 4, indicating that we want to find the 4th root of 16. The `find_nth_root` function is then invoked with these parameters, and the calculated nth root is stored in the variable `result`.

Finally, a formatted string is used to display `The 4th root of 16 is: 2.0`.

## Find the NTH Root of X Value in Python Using `math.pow()`

The `math.pow()` function in Python is part of the `math` module. It takes two arguments, the base and the exponent, and returns the result of raising the base to the power of the exponent.

The syntax is as follows:

``````result = math.pow(base, exponent)
``````

Here, `base` is the number you want to raise to a power, and `exponent` is the power to which you want to raise the base.

To find the nth root of a number x, we can use the `math.pow()` function by raising x to the power of (1 / n). The formula is as follows:

``````nth_root = math.pow(x, 1 / n)
``````

Here, `x` is the value for which we want to find the nth root, and `n` is the degree of the root.

Let’s illustrate this with an example:

``````import math

def find_nth_root(x, n):
nth_root = math.pow(x, 1 / n)
return nth_root

x = 16
n = 4

result = find_nth_root(x, n)
print(f"The {n}th root of {x} is: {result}")
``````

Output:

``````The 4th root of 16 is: 2.0
``````

The provided code begins by importing the `math` module, which contains `math.pow()` that we utilized to calculate the nth root. The `find_nth_root` function is defined, taking two arguments: `x` (the number for which we want to find the nth root) and `n` (the degree of the root we’re seeking).

Inside this function, `math.pow(x, 1 / n)` is employed to calculate the nth root of `x` by raising `x` to the power of `1 / n`. This value is assigned to `nth_root`, which is then returned.

In the example usage, `x` is set to 16, representing the number for which we want to calculate the nth root. `n` is set to 4, indicating that we’re looking for the 4th root of 16.

The `find_nth_root` function is called with these parameters, and the calculated nth root is stored in the variable `result`.

Finally, a formatted string is used to display the result, showcasing the 4th root of 16.

## Find the NTH Root of X Value in Python Using `math.exp()` and `math.log()`

The formula for finding the nth root of a number x can also be represented in terms of the exponential and logarithmic functions as:

``````nth root value = exp(log(x) / n)
``````

Here, `exp` is the exponential function, and `log` is the natural logarithm function.

In Python, the `math` module provides the necessary functions `exp()` and `log()` to implement this formula and calculate the nth root of a value `x`.

Let’s go through an example code and understand how to use this formula effectively.

``````import math

def nth_root(x, n):
nth_root_value = math.exp(math.log(x) / n)
return nth_root_value

x = 64
n = 3

nth_root_value = nth_root(x, n)
print(f"The cube root of {x} is: {nth_root_value}")
``````

Output:

``````The cube root of 64 is: 4.0
``````

Here, we begin by importing the `math` module, which provides the `exp()` and `log()` functions needed for our calculation.

Then, we define a function `nth_root` that takes two parameters, `x` (the value for which we want to find the nth root) and `n` (the desired root). Inside the function, we calculate the nth root using the formula `exp(log(x) / n)` and return the result.

As an example, we set the value of `x` to 64 and the desired root `n` to 3 (e.g., cube root). We then call the `nth_root` function with these values and store the result in `nth_root_value`.

Finally, we print the result, showing the nth root of `x` (here, the cube root of 64).

## Conclusion

Calculating the nth root of a number is a common operation in various mathematical and scientific applications. In Python, we have multiple ways to achieve this, including using the exponentiation operator, the `math` module, or the `numpy` library.

Depending on the requirements and the nature of the project, you can choose the most suitable method for finding the nth root of `x` in Python.

Author: Abdul Jabbar

Abdul is a software engineer with an architect background and a passion for full-stack web development with eight years of professional experience in analysis, design, development, implementation, performance tuning, and implementation of business applications.