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This is a somewhat funny question. To explain the problem of complex extensions of the principal square root, I would like to have two visibly different square root signs within the same document; for example, besides the usual one, a boldface square root sign, yet hosting a normally typed argument. I have no clues. If not possible, I would be grateful for suggestions about totally different solutions...

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Yes of course this can be done with the bm package. The usage is detailed in the package documentation section 3.3.

\documentclass{article}
\usepackage{amsmath}
\usepackage{bm}

\begin{document}

$\bm\sqrtsign{x} \quad \text{vs.} \quad \sqrt{x}$

\end{document}

enter image description here

However, I would urge you to come up with something a little bit more noticeable.

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    strange as it may seem, I can be wrong (especially this time of night:-) I think I'll delete my answer in that case Commented May 4, 2017 at 22:41

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