%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-7-8 on page II-200 in "Radical movements".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See https://www.latex-project.org/lppl.txt for details.
%%

\documentclass{tlc3examargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{111.0pt}

  % Shorten the vertical size of the example ...
  \AtBeginDocument{%
    \setlength\abovedisplayskip{.5\abovedisplayskip}%
    \setlength\belowdisplayskip{.5\belowdisplayskip}%
  }

%StartShownPreambleCommands
\usepackage{amsmath}
%StopShownPreambleCommands

\begin{document}
\[ \sqrt[\beta]{k}                        \qquad
   \sqrt[\leftroot{2}\uproot{4} \beta]{k} \qquad
   \sqrt[\leftroot{1}\uproot{3} \beta]{k}        \]
\end{document}