Floating point square root symbol

Question

For my numerical analysis class, we use a certain symbol to represent the floating point square root operation (similar to using \ominus for floating point subtraction, \oplus for floating point addition, etc.). In order to render this in a LaTeX document, I'd need to somehow draw a similarly-sized circle over the "v" part of the square root symbol, but I'm not too familiar with tikz and don't really know how to start working on this.

The most important aspect is making sure the circle has the same size as the one for the \oxxxx symbols. How would I go about making this? (And potentially, is there a better, more standard way to denote this operation?)

Picture

Edit

Added a picture to make what I'm asking for a tiny bit clearer.

Answer 1

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}

Answer 2

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}