nthroot

Real nth root of real numbers

Syntax

Y = nthroot(X,N)

Description

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

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 = 1×3

   -1.5157   -2.0000   -0.1250

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

Element-wise Roots of Matrix

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

X = [-2 -2 -2; 4 -3 -5]

X = 2×3

    -2    -2    -2
     4    -3    -5

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

N = 2×3

    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 = 2×3

   -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. 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 | table | timetable

N — Roots to calculate

scalar | array, table, or timetable of same size as X

Roots to calculate, specified as a scalar or array, table, or timetable 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 | 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.

This 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™.

This function fully supports GPU arrays. 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

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.