Why is there a space between the left parenthesis and the radical sign?

Question

Minimal working example:
documentclass{article}

begin{document}
Default spacing: ((sqrt 2))

Negative space after the left parenthesis: ((!sqrt 2))
end{document}

To me, the default spacing looks bad, and it looks better to remove space after the left parenthesis. Is there any reason not to do so? Why is it the default in the first place?

egreg · Accepted Answer

It's an optical effect. There is no space added between ( and the surd:
documentclass{article}

newcommand{zw}{kern-0.05ptvrule width0.1ptkern-0.05pt}

begin{document}

((zwsqrt{2}))

((sqrt{2}))

end{document}

The fact is that the construction is asymmetric; the effect is less visible with a symmetric symbol such as x:

Instead of reducing the space in front of the radical (in any case ! is too drastic), increase the space after it, particularly if a parenthesis follows.
documentclass{article}
usepackage{amsmath}

begin{document}

((sqrt{2}))

((sqrt{2},))

((mspace{-1.5mu}sqrt{2}))

end{document}

Why is there a space between the left parenthesis and the radical sign?

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