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# nthroot

Real nth root of real numbers

## Description

example

Y = nthroot(X,N) returns the real nth root of the elements of X. Both X and N must be real scalars or arrays of the same size. If an element in X is negative, then the corresponding element in N must be an odd integer.

## Examples

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### Calculate Real Root of Negative Number

Find the real cube root of -27.

`nthroot(-27, 3)`
```ans =

-3```

For comparison, also calculate (-27)^(1/3).

`(-27)^(1/3)`
```ans =

1.5000 + 2.5981i```

The result is the complex cube root of -27.

### Calculate Several Real Roots of Scalar

Create a vector of roots to calculate, N.

`N = [5 3 -1];`

Use nthroot to calculate several real roots of -8.

`Y = nthroot(-8,N)`
```Y =

-1.5157   -2.0000   -0.1250```

The result is a vector of the same size as N.

### Elementwise Roots of Matrix

Create a matrix of bases, X, and a matrix of nth roots, N.

```X = [-2 -2 -2; 4 -3 -5]
N = [1 -1 3; 1/2 5 3]```
```X =

-2    -2    -2
4    -3    -5

N =

1.0000   -1.0000    3.0000
0.5000    5.0000    3.0000```

Each element in X corresponds to an element in N.

Calculate the real nth roots of the elements in X.

`Y = nthroot(X,N)`
```Y =

-2.0000   -0.5000   -1.2599
16.0000   -1.2457   -1.7100```

Except for the signs (which are treated separately), the result is comparable to abs(X).^(1./N). By contrast, you can calculate the complex roots using X.^(1./N).

## Input Arguments

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### X — Input arrayscalar | vector | matrix | multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array. X can be either a scalar or an array of the same size as N. The elements of X must be real.

Data Types: single | double

### N — Roots to calculatescalar | array of same size as X

Roots to calculate, specified as a scalar or array of the same size as X. The elements of N must be real. If an element in X is negative, the corresponding element in N must be an odd integer.

Data Types: single | double