[Tex/LaTex] How to write a reflected \sqrt operator

Question

How can I produce this symbol in LaTeX? It is used in Galois theory for p-adic fields to denote a root of the equation X^{p}-X-a with a \in k, and being k a p-adic field. I have tried a lot of different things like rotatebox or reflect box, but I can't produce the same output.

Answer 1

\documentclass{article}
\usepackage{graphicx}
\newcommand\reflectsqrt[2][\relax]{
  \ifx\relax#1
    \scalebox{1}[-1]{$\sqrt{\scalebox{1}[-1]{$#2$}}$}
  \else
    \scalebox{1}[-1]{$\sqrt[{\scalebox{1}[-1]{%
      \raisebox{-4pt}{$\scriptscriptstyle#1$}}}]{\scalebox{1}[-1]{$#2$}}$}
  \fi
}
\begin{document}
$x\reflectsqrt{a}$

$x\reflectsqrt[p]{a_3 + b^3}$
\end{document}