# Root Calculator

Welcome to our **root calculator**, a simple tool to calculate the **nth root** of any real number. Whether you want to calculate **square root** or **fourth root**, our nth root calculator has you covered. In this article, we shall discuss the nth root and how to calculate it, so keep scrolling and find out more.

## nth root

The nth root of a real number *a* is the number we must raise to the power *n* to produce *a*. Mathematically, we express this as:

Where $x$, $n$ and $a$ are all real numbers. $x$ is the nth root of $a$.

For example, the 4 is the 3rd root of the number 64, because $4 \times 4 \times 4 = 64$.

🔎 Both the **root operator** and **logarithm function** are related to the **exponent operator**. You will notice the subtle difference between these two by learning more about the log function.

## Calculating square root

The 2nd root of a number is so common that it has its unique name - **square root**. One method to find the square root of a number involves prime factorizing the number and looking for pairs of primes. Consider the number 81.

**Prime factorize**81 to get:

- Look for
**pairs**of**primes**. We can gather two pairs of 3s:

- Apply the
**square root**. For each pair, we shall get one prime out of the square root.

**Multiply**the**remaining numbers**together to get the answer:

- Verify this result with our root calculator, which can also function as a square root calculator!

We use square roots everywhere, especially in geometry. Find out its crucial role in determining one side of a right triangle from the other two sides using our Pythagorean theorem calculator.

## Calculating nth root

Calculating the nth root is similar to calculating a square root. The only change after prime factorization is we must look for groups of *n* primes instead of *2*. For example, calculating the fourth root of 81 will give us:

Notice that calculating the fourth root of a number is the same as finding the square root of the square root of the number!

## How to use this root calculator

This nth root calculator is straightforward to use:

- Enter the number
`a`

for which you seek the nth root. - Enter the value of
`n`

. - Our root calculator will automatically display the nth root of the number a.
- To use it as a square root calculator, enter
`2`

as the value for`n`

.