How do I slant the Computer Modern root symbol?

Question

Considering this question, actually I not remember as I must straighten square root symbol to have the classic sqrt symbol. I have used (for example),

\def\mySqrt{\radical"0270373\relax}

but it not works. I not remember if I must to use \mathstrut, \smash or other....

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\def\mySqrt{\radical"0270373\relax}
\begin{document}
    \begin{equation}
        w_{n} = \frac{1}{N_d}\mySqrt{\frac{2\epsilon_{s}V_{bi}}{q\left( \dfrac{1}{N_a} + \dfrac{1}{N_d}\right)}}
    \end{equation}
\end{document} 

Edit: 2021/11/27

Why CM font give us a ugly, sometimes, root (not slanted) instead of other fonts? What is the reason?

Answer 1

If your document allows using the mtpro2 math font package, you could make use of that package's \SQRT macro to get square-root symbols with sloping surds [am I using the term "surd" correctly?], as long as the total height of the argument of \SQRT does not exceed 4", or 10 cm. The formulas in your publications will never contain such a monstrosity, though, right?

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\usepackage[lite]{mtpro2}
\begin{document}
\[
\sqrt{\frac{2\epsilon_{s}V_{bi}}{q\left( \dfrac{1}{N_a} + \dfrac{1}{N_d}\right)}}
\quad\mbox{vs.}\quad
\SQRT{\frac{2\epsilon_{s}V_{bi}}{q\left( \dfrac{1}{N_a} + \dfrac{1}{N_d}\right)}}
\qquad
\SQRT{\dfrac{\dfrac{\dfrac{\dfrac{8}{8}}{\dfrac{8}{8}}}{\dfrac{\dfrac{8}{8}}{\dfrac{8}{8}}}}{\dfrac{\dfrac{\dfrac{8}{8}}{\dfrac{8}{8}}}{\dfrac{\dfrac{8}{8}}{\dfrac{8}{8}}}}}
\]
\end{document}

Answer 2

With unicode-math (in LuaLaTeX or XeLaTeX), you can replace the radical symbol with any other OpenType math font’s. One of the few with a slanted radical is Garamond Math:

\documentclass{article}
\usepackage{unicode-math}
\usepackage{newcomputermodern}

\setmathfont{Garamond Math}[range=\surd,
                            Scale=MatchUppercase]

\begin{document}
    \begin{equation*}
        w_{n} = \frac{1}{N_d}\sqrt{\frac{2\epsilon_{s}V_{bi}}{q\left( \dfrac{1}{N_a} + \dfrac{1}{N_d}\right)}}
    \end{equation*}
\end{document} 

To better match the weight, I use New Computer Math Book.

Answer 3

This doesn't supply a large radical symbol with a slanted stroke as requested in the question, but at the request of the OP, addresses the history of the shape in the Computer Modern fonts.

As with so many things in TeX and CM, the reason for the vertical stroke when the height exceeds a certain amount is the limited memory available when TeX was created, along with the limited capabilities of available imaging devices.

A vertical stroke can be extended easily by adding small vertical segments, which will line up automatically. Controlling the extension of a sloped line is much more complicated. It involves not only supplying a segment in the font, but also the mechanism for joining successive segments precisely. In fact, it is likely that more than one such segment, at different angles, would have to be provided, in the absence of the ability to redraw the symbol at the time of imaging. Only "static" shapes were possible when TeX was created.