Customised radical-sign

Question

I've been trying to customise the shape of radical sign

so that it looks slimmer with the left protrusion consuming little space.

And this is my attempt:

\documentclass{standalone}
\makeatletter
\RequirePackage{epic}
\RequirePackage{eepic}
\def@drawradical#1#2{% #1: total height, #2: width of radical
\begingroup
@tempdima#1\p@ @tempdimb#2\p@
\dimen@-.9@tempdima
\edef@radical@coordAx{0}%
\edef@radical@coordAy{\strip@pt\dimen@}%
\dimen@.1@tempdimb \dimen@ii-.75@tempdima
\edef@radical@coordBx{\strip@pt\dimen@}%
\edef@radical@coordBy{\strip@pt\dimen@ii}%
\dimen@.4@tempdimb \dimen@ii-@tempdima
\edef@radical@coordCx{\strip@pt\dimen@}%
\edef@radical@coordCy{\strip@pt\dimen@ii}%
\dimen@\fontdimen8\textfont3\relax
\edef@sqrt@linethickness{\strip@pt\dimen@\space}%
\dimen@-1.5\dimen@
\edef@radical@coordDx{\strip@pt@tempdimb}%
\edef@radical@coordDy{\strip@pt\dimen@}%
\unitlength1pt
\begin{picture}(0,0)
\drawline(@radical@coordAx,@radical@coordAy)(@radical@coordBx,@radical@coordBy)
\drawline(@radical@coordCx,@radical@coordCy)(@radical@coordDx,@radical@coordDy)
\thicklines
\drawline(@radical@coordBx,@radical@coordBy)(@radical@coordCx,@radical@coordCy)
\end{picture}
\endgroup}
\def@sqrt@divide#1/#2{%
\ifdim#1<32\p@
\multiply#1 256\relax \divide#2 256\relax
\else
\ifdim#1<64\p@
\multiply#1 128\relax \divide#2 512\relax
\else
\ifdim#1<128\p@
\multiply#1 64\relax \divide#2 1024\relax
\else
\ifdim#1<256\p@
\multiply#1 32\relax \divide#2 2048\relax
\else
\ifdim#1<512\p@
\multiply#1 16\relax \divide#2 4096\relax
\else
\multiply#1 8\relax \divide#2 8192\relax
\fi
\fi
\fi
\fi
\fi
\divide#1 by #2\relax}
\DeclareRobustCommand{\sqrt}{@testopt@sqrt{}}
\def@sqrt[#1]#2{%
{@save@counters
\mathchoice
{@@sqrt\displaystyle    {#1}{#2}}%
{@@sqrt\textstyle        {#1}{#2}}%
{@@sqrt\scriptstyle      {#1}{#2}}%
{@@sqrt\scriptscriptstyle{#1}{#2}}}}
\def@@sqrt#1#2#3{%
\hbox{%
@restore@counters
\setbox\z@\hbox{\m@th$#1#3$}%
\dimen@\ht\z@  \advance\dimen@\p@
\dimen@ii\dp\z@ \advance\dimen@ii\p@
\setbox\z@\hbox{\m@th$#1%
\overline{%
\box\z@
\vrule@width\z@ @height\dimen@ @depth\dimen@ii}$}%
\dimen@\ht\z@ \advance\dimen@\dp\z@
\ifx#1\scriptscriptstyle \let@tempa\ssf@size
\else
\ifx#1\scriptstyle    \let@tempa\sf@size
\else                \let@tempa\tf@size
\fi
\fi
\dimen@ii@tempa\p@ \dimen@ii.5\dimen@ii
\edef@tempa{\noexpand@drawradical
{\strip@pt\dimen@}{\strip@pt\dimen@ii}}%
\setbox4\hbox{\raise\ht\z@\hbox to\dimen@ii{@tempa\hfil}}%
\def@tempa{#2}%
\ifx@tempa@empty
\box4\relax
\else
\setbox\tw@\hbox{\m@th$\scriptscriptstyle #2$\hskip.5\dimen@ii}%.25-->.5
\dimen@\ht\z@ \advance\dimen@-\ht\tw@
\setbox\tw@\hbox{\raise.5\dimen@\box\tw@}%%.6-->.5 2017-10-18
\ifdim\wd4<\wd\tw@ \box\tw@ \llap{\box4}%
\else              \box4    \llap{\box\tw@}%
\fi
\fi
\box\z@}}
\def@save@counters{%
\def@elt##1{\noexpand\setcounter{##1}{\number\csname c@##1\endcsname}}%
\edef@restore@counters{\cl@@ckpt}}
%\endinput
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\makeatother
\begin{document}
$\sqrt{10}$
\end{document}

which produces the result:

Apparently, the diagonal lines are not connected smoothly at both ends.

How can I solve this problem?

I need to seek your advice.

Thank you.