Mirrored Cube Rooted Fraction Looks Weird

Question

I was testing something with Overleaf, and then a weird result was output.

What's more weird is that I went to a Discord server where a TeX-rendering engine exists. This is its result:

It's a really simple piece of code:

\Huge$$\sqrt[3]{\frac{100}{300}}$$

While This one looks better, I like how the first one appears. How can I keep the look of the first cube root, but also align the 3 properly? Also, why's this happening?

UPDATE: This question is related to the original one.

I defined a new command that is a mirror of the root (\newcommand{\asqrt}[2][1]{\reflectbox{\ensuremath{{\sqrt[#1]{#2}}}}}) in the preamble. Its size is smaller than the normal root:

Here's how I call both of them: \Huge\[\ \sqrt[n]{\frac{100}{300}} \quad \asqrt[n]{\frac{100}{300}}\]\

Why are they different?

Answer 1

Almost any document using math should load amsmath which provides many additional math features and corrects this

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\Huge
a
\[\sqrt[3]{\frac{100}{300}}\]
\end{document}

If you want the straight form use the cmex10 option

\documentclass{article}
\usepackage[cmex10]{amsmath}
\begin{document}

\Huge
a
\[\sqrt[\leftroot{6}\uproot{-6}3]{\frac{100}{300}}\]
\end{document}

---

With either definition, you can add a reflectbox in a mathpalette so it works in all styles

\documentclass{article}
\usepackage[cmex10]{amsmath}
\usepackage{graphicx}
\newcommand\asqrt[1][]{\mathpalette{\aasqrt{\sqrt[#1]}}}
\makeatletter
\newcommand\aasqrt[3]{\reflectbox{$\m@th#2#1{#3}$}}
\makeatother
\begin{document}

\Huge 

$\sqrt{x} \qquad \asqrt{x}$


$\sqrt[3]{x} \qquad \asqrt[3]{x}$

a
\[
\sqrt[\leftroot{6}\uproot{-6}3]{\frac{100}{300}}
\qquad
\asqrt[\leftroot{6}\uproot{-6}3]{\frac{100}{300}}
\]
\end{document}

Answer 2

I took the question to mean you wanted the \surd more vertically oriented.

What I do is vertically stretch the argument 50% before applying the square root. The greater height makes the \surd orient itself more vertically. Then I vertically compress the result back to its original scale. Note the root degree (optional argument) needs to be stretched separately, so that the recompression brings it back to proper scale.

\documentclass{article}
\usepackage{scalerel,amsmath}
\newcommand\xsqrt[2][]{%
  \vstretch{.666}{\sqrt[\vstretch{1.5}{#1}]{\vstretch{1.5}{\!#2}}}
}
\begin{document}
\Huge
\[
x\xsqrt[3]{\frac{100}{300}}
\]
\end{document}