# surd

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```surd(`x`, `n`)
```

## Description

For a complex number `x` and integer `n`, ```surd(x, n)``` returns the n-th root of x whose (complex) argument is closest to that of `x`.

If `x` is a positive real number, ```surd(x, n)``` coincides with `x^(1/n)`. If `x` is a negative real number and `n` is odd, then ```surd(x, n)``` coincides with `-|x|^(1/n)`.

`surd(x, n)` returns that complex solution y of yn = x with polar angle closest to that of x; among two equally distant y's, the one with smaller argument is chosen. In contrast, `x^(1/n)` represents the solution with the smallest absolute value of the polar angle in the range .

If `n` is a numerical value, it must be a non-zero integer. If it is symbolic, it is understood to represent a non-zero integer.

`surd(x, 2)` is mathematically equivalent to `sqrt(x)`. Unlike `sqrt`, however, `surd` may return an unevaluated symbolic call.

## Environment Interactions

When called with a floating-point argument, the function is sensitive to the environment variable `DIGITS` which determines the numerical working precision.

## Examples

### Example 1

If n is odd and x is real, then `surd(x, n)` is real, too. On the other hand, `x^(1/n)` is not real if x is negative:

`surd(-27, 3), surd(-27.0, 3), (-27)^(1/3), (-27.0)^(1/3)`

### Example 2

`surd` may be called with symbolic arguments:

`surd(3, n)`

Sometimes, `surd` returns an unevaluated function call:

`surd(x, 3), surd(x, n^2 + n)`

## Parameters

 `x` `n`

## Return Values

Arithmetical expression.