This code
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ J(\sqrt[n]{x}) \]
\end{document}
compiles into this:

The spacing after the opening parentheses is ugly. What's the proper way to fix this?
This code
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ J(\sqrt[n]{x}) \]
\end{document}
compiles into this:

The spacing after the opening parentheses is ugly. What's the proper way to fix this?
There is really a difference between J(\sqrt{x}) and J(\sqrt[n](x)), that's not justified by the root index: a small horizontal space is added in the latter case.
You can get the same width by patching the \sqrt command:
\documentclass{article}
\usepackage{amsmath}
\usepackage{xpatch}
\makeatletter
\xpatchcmd{\sqrt}{\@sqrt}{{\mspace{-2.9274mu}\@sqrt}}{}{}
\makeatother
\begin{document}
\sbox0{$J(\sqrt{x})$}\the\wd0
\sbox0{$J(\sqrt[n]{x})$}\the\wd0
\[ J(\sqrt{x})+J(\sqrt[n]{x})\]
\end{document}

There will still be some more space in script style, though.
However, proper typesetting of this requires a thin space after the radical:
J(\sqrt[n]{x}\,)
so the output would be

Such adjustment can't be provided automatically, because it depends on the symbol following the radical.
amsmath.
– egreg
Jan 29 '15 at 22:49
-2.9274mu number? Where did it come from? (Can I calculate it based on something else?)
– user541686
Jan 29 '15 at 22:50
\mspace{-2.9274mu} rather than \mkern-2.9274mu as the spacing adjustment directive?
– Mico
Jul 12 '15 at 07:02
J(\!\sqrt[n]{x})? – Manuel Jan 29 '15 at 20:58\sqrt? Doesn't seem like a good solution... – user541686 Jan 29 '15 at 20:59\,between the radical and the closing parenthesis:J(\!\sqrt[n]{x}\,)– egreg Jan 29 '15 at 21:01(\sqrtby(\!\sqrtand that's probably it. – Manuel Jan 29 '15 at 21:07\sqrtcommand, may be it's doable, but it doesn't seem too obvious. – Manuel Jan 29 '15 at 21:16