Floating point square root symbol

I can offer this one, but don't try it with big arguments to the square root such as fractions.

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}

\newcommand{\fpsqrt}[1]{%
  \sqrt[\leftroot{-5}\uproot{-7}\scalebox{0.7}{$\bigcirc$}]{\mathstrut#1}%
}

\begin{document}

\[
\fpsqrt{120}
\]

\end{document}

This is really just for fun (and because this is tagged TikZ). An attempt to adapt the shape of the circle to the dimensions of the square root. The idea is to use a path picture to find out what the dimensions of the square root are. Luckily tikzmark has the cool feature of detecting the mode we are in, so we do not have to worry about this here.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{tikzmark,calc}
\newcounter{stuff}
\tikzset{oroot/.style={path picture={\draw
let \p1=($(path picture bounding box.north)-(path picture bounding box.south)$) in (path picture bounding box.west)
arc(180:-180:{0.25em+\y1/10} and \y1/3);}}}
\begin{document}
abc  $\tikzmarknode[oroot]{1}{\sqrt{a+b}}$
\[\tikzmarknode[oroot]{2}{\sqrt{\frac{\frac{1}{12}}{\frac{a}{b}}}}\]
\end{document}