# nroot

A function that calculates the nth root of an object

Controller: **samtheman**

**Contents**

## Interface

C++

## Nroot

template<class T> Tnroot( | const T& | x | |

const T& | n | ) |

*x*, as in , using the iterative formula This algorithm converges quadratically, meaning that the bits of precision double per iteration, resulting in 64 bits after 6 iterations, which is the number of iterations used in the function. pow(const T&, const E&) must be defined and the normal arithmetic operators must accept different combinations of T and E.

### Example 1

#include <stdio.h> using namespace Maths::Arithmetic; int main() { for(double x = 10; x <= 100; x += 10) //to resolve pow ambiguities { for(int y = 2; y < 5; y++) printf("The %d root of %.0f is %lf\n", y, x, nroot(x,y)); } return 0; }

### Output

The 2 root of 10 is 3.162278 The 3 root of 10 is 2.154435 The 4 root of 10 is 2.632547 The 2 root of 20 is 4.472136 The 3 root of 20 is 2.714418 The 4 root of 20 is 2.114743 The 2 root of 30 is 5.477226 The 3 root of 30 is 3.107233 The 4 root of 30 is 2.340347 The 2 root of 40 is 6.324555 The 3 root of 40 is 3.419952 The 4 root of 40 is 2.514867 The 2 root of 50 is 7.071068 The 3 root of 50 is 3.684031 The 4 root of 50 is 2.659148 The 2 root of 60 is 7.745967 The 3 root of 60 is 3.914868 The 4 root of 60 is 2.783158 The 2 root of 70 is 8.366600 The 3 root of 70 is 4.121285 The 4 root of 70 is 2.892508 The 2 root of 80 is 8.944272 The 3 root of 80 is 4.308869 The 4 root of 80 is 2.990698 The 2 root of 90 is 9.486833 The 3 root of 90 is 4.481405 The 4 root of 90 is 3.080070 The 2 root of 100 is 10.000000 The 3 root of 100 is 4.641589 The 4 root of 100 is 3.162278

### Note

- This function does not check for what would be normally incorrect input, as some objects are meant to act differently than normal numbers, such as complex numbers. If incorrect input values are passed to the function, the return values will be junk.

### References

- "Nth root algorithm." Wikipedia, The Free Encyclopedia. 8 Feb 2007, 14:48 UTC. Wikimedia Foundation, Inc. 3 Jun 2007 http://en.wikipedia.org/w/index.php?title=Nth_root_algorithm&oldid=106578515

### Parameters

x a number n the root required

### Returns

- to nth root of inval

### Authors

*Sam Schetterer (June 2007)*

##### Source Code

Source code is available when you agree to a GP Licence.

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Last Modified: 2 Jan 08 @ 20:28 Page Rendered: 2022-03-14 17:36:46