# nthRoot() Function & Examples

Use the nthRoot() arithmetic function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

## nthRoot

#### nthRoot(a)

#### nthRoot(a, root)

Try it yourself:

```calculio
4 ^ 3
nthRoot(64, 3)
nthRoot(9, 2)
sqrt(9)
```

[pow](https://calcul.io/function/pow/index.md)

[sqrt](https://calcul.io/function/sqrt/index.md)

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## Calculate a principal nth root

**nthRoot(x, n)** returns an nth root of x. It generalizes [sqrt](https://calcul.io/function/sqrt/index.md), which is the second root, and [cbrt](https://calcul.io/function/cbrt/index.md), the cube root.

## Example

`nthRoot(81, 4)` is 3. It is useful for reversing powers, scaling laws, and geometric formulas. Use [pow](https://calcul.io/function/pow/index.md) to verify that raising the result to n returns the input where the branch convention allows it.

## Domain cautions

For real arithmetic, even roots of negative values are not real, while odd roots can be. Complex inputs have branch choices, so the returned result is a principal root rather than every possible answer. Use [nthRoots](https://calcul.io/function/nthRoots/index.md) when all complex roots are required. The degree should be a meaningful nonzero integer.

[All functions](https://calcul.io/functions/index.md)