English

Denesting cubic radicals

General Mathematics 2024-10-01 v2

Abstract

We study in details how and when the radical a+bp3\sqrt[3]{a+b\sqrt p} with rational numbers a,ba,b and pp positive can be simplified, providing a complete answer to the problem; furthermore, a program that computes the result is also made available. The solution highlights an interesting connection with the cubic formula.

Keywords

Cite

@article{arxiv.2403.04776,
  title  = {Denesting cubic radicals},
  author = {Alberto Cavallo},
  journal= {arXiv preprint arXiv:2403.04776},
  year   = {2024}
}