scaling root problem

Question

Background [TL;DR]

In my previous meta question Vertical space between superscript and square root sign, I attempted (not so successfully) to illustrate a display problem about the square root sign by $\sqrt{e^\overline{X}}$: $\sqrt{e^\overline{X}}$.

I had thought about enlarging this: ${\Huge \sqrt{e^\overline{X}}}$: ${\Huge \sqrt{e^\overline{X}}}$, but the stroke going northeast $\nearrow$ surpasses the horizontal stroke going to the right-hand side $\to$.

Screenshot using Opera 71 on Ubuntu 20.04 LTS

MWE (min. working example)

$$\sqrt{a}$$
$$\Large{\sqrt{a}}$$
$$\Huge{\sqrt{a}}$$

$$\sqrt{a}$$ $$\Large{\sqrt{a}}$$ $$\Huge{\sqrt{a}}$$

Screenshot

Screenshot taken by Firefox 84.0.1 on Ubuntu 20.04 LTS

Expected output

The right-upward directed stroke $\nearrow$ and the horizontal stroke $\to$ are perfectly joined together as shown in the following image, but without the vertical stroke $\downarrow$.

image source: Badly scaling closing SQRT symbol with large font sizes on $\rm\TeX$.SE

Answer 1

Neither a solution nor an analysis of the inner working of MathJax. Just posting

${\sqrt{\Huge{e^\overline{X}}}}$

for comparison:

${\sqrt{\Huge{e^\overline{X}}}}$

This looks better on my screen (Firefox, version 84), but may be is not quite what you wanted.