General Approach of the Root of a P-Adic Number

Kecies Mohamed, Zerzaihi Tahar

In this work, we applied the Newton method in the p-adic case to calculate the cubic root of a p-adic number $a\in \Bbb Q^*_p$ where $p$ is a prime number, and through the calculation of the approximate solution of the equation $x^3-a=0$. We also determined the rate of convergence of this method and evaluated the number of iterations obtained in each step of the approximation.