Ah.
This can not possibly be a bug, so it must be a (only slightly) documented feature.
As mentioned in the bm
manual, commands with optional arguments are locally modified inside \bm
specifically so that \bm{\sqrt{xyz}}
works. To see why you need \bm{{\sqrt{...}}}
with an extra pair of braces in your example, consider:

\documentclass{article}
\usepackage{bm}
\showoutput
\begin{document}
$\sqrt{1x}$
$\sqrt{2x^2}$
$\sqrt{3x\strut^2}$
$\bm{\sqrt{4x^2}}$
$\bm{\sqrt{5x}}$
$\bm{{\sqrt{6x^2}}}$
\boldmath
$\sqrt{7x^2}$
$\sqrt{8x\strut^2}$
\end{document}
Looking at the relevant bit of the log file
$ grep \\\\OM[SX] bm111.log
......\OMS/cmsy/m/n/10 p
......\OMS/cmsy/m/n/10 p
......\OMX/cmex/m/n/5 q
......\OMS/cmsy/b/n/10 p
......\OMS/cmsy/b/n/10 p
.........\OMS/cmsy/b/n/10 p
......\OMS/cmsy/b/n/10 p
......\OMX/cmex/m/n/5 q
You can see that "small" radicals come from the symbol font OMS/cmsy/m
which has a bold version installed OMS/cmsy/b
but large radicals come from the symbol extension font OMX/cmex/m
which in the standard Computer Modern font set doesn't have a bold version.
Your case with a superscripted capital is on a tipping point, if bm
sets it all together (due to the extra braces) the cramped style is used, the radical gets chosen from cmsy and goes bold, but without the extra help the radical comes from cmex for which there is no bold font.
amsmath
? If yes, you need to put the\sqrt{}
macro in braces, like this:$\bm{A={\sqrt{B^2+C^2}}}$
. Then it'll work. See page 9 of thebm
manual. – Old Nick Dec 11 '13 at 11:17{}
in both cases. I tried only the working cases without amsmath (like\sqrt{C}
) and they obviously worked. This, plus I think I misread the referenced page. – Old Nick Dec 11 '13 at 12:28