nthroot

Real nth root of real numbers

Syntax

Y = nthroot(X,N)

Description

Y = nthroot(X,N) returns the real nth root of X. If an element in X is negative, then the corresponding element in N must be an odd integer.

Examples

Real Root of Negative Number

Find the real cube root of -27.

nthroot(-27,3)

ans = 
-3

For comparison, calculate (-27)^(1/3). The result is the complex cube root of -27.

(-27)^(1/3)

ans = 
1.5000 + 2.5981i

Real Roots of Scalar

Calculate several real nth roots of -8.

N = [5 3 -1];
Y = nthroot(-8,N)

Y = 1×3

   -1.5157   -2.0000   -0.1250

Real Roots of Vector

Create a row vector of bases, X, and a column vector of roots to calculate, N.

X = [4 -3 -5];
N = [1; -1; 3];

Calculate the real nth roots of the elements in X. The result is a matrix containing all combinations of bases and roots. For example, Y(3,1) is the 3rd root of 4.

Y = nthroot(X,N)

Y = 3×3

    4.0000   -3.0000   -5.0000
    0.2500   -0.3333   -0.2000
    1.5874   -1.4422   -1.7100

Element-Wise Roots of Matrix

Create a matrix of bases, X, and a matrix of roots to calculate, N. Each element in X corresponds to an element in N.

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

Calculate the real nth roots of the elements in X.

Y = nthroot(X,N)

Y = 2×3

   -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

X — Input array

scalar | vector | matrix | multidimensional array | table | timetable

Input array, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. The elements of X must be real. Inputs X and N must either be the same size or have sizes that are compatible.

Data Types: single | double | table | timetable

N — Roots to calculate

scalar | vector | matrix | multidimensional array | table | timetable

Roots to calculate, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. The elements of N must be real. If an element in X is negative, the corresponding element in N must be an odd integer. Inputs X and N must either be the same size or have sizes that are compatible.

• If X is a multidimensional array, N cannot be a table or timetable.

• If X is a table or timetable, then N can be the same data type as X or a scalar, vector, matrix, or multidimensional array of a compatible size. If both inputs are tables or timetables, then see Rules for Table and Timetable Mathematics for the input requirements.

Data Types: single | double | table | timetable

Tips

• While power is a more efficient function for computing the roots of numbers, in cases where both real and complex roots exist, power returns only the complex roots. In these cases, use nthroot to obtain the real roots.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

The nthroot function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The nthroot function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2023b: Support for implicit expansion of arguments

nthroot supports implicit expansion of the input arguments X and N. For more information on the required input sizes, see Compatible Array Sizes for Basic Operations.

If your code relies on the errors that MATLAB^® previously returned for mismatched sizes, particularly within a try/catch block, then your code might no longer catch those errors.

R2023a: Perform calculations directly on tables and timetables

The nthroot function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.