I'd recommend the following:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
$\sqrt{\smash[b]{1\! \underbrace{44\cdots4\,}_\text{$n$ times}}}$
\end{document}
Note that it's syntactically cleaner to place $n$ times
inside a \text
macro. The \smash[b]
command "hides" the stuff below the baseline from TeX, inducing it not to make the lower end of square-root symbol plunge down to far. The \!
instruction removes the unnecessary whitespace otherwise inserted by the left-hand end of the underbrace, while \,
serves to avoid a clash between the right-hand end of the underbrace and the final 4
. Finally, and I realize that some will disagree with me, I think it's better to use \cdots
than \ldots
in this case.
Addendum: This MWE was meant to produce an image of a single formula in which the "root" of the square-root symbol doesn't plunge down unnecessarily far. If this formula were part of some longer running text, a problem would immediately arise: the following line of text and math -- and, depending on the depth of the underbrace contents, even the line after that -- will run smack over the underbrace material. As @egreg notes in his comment and as @Werner shows in his answer, to keep this from happening the formula should be augmented to contain a \vphantom
outside the square-root that has the exact same depth as the formula would have if \smash
weren't being used. This may be done, e.g., as follows:
$\vphantom{\underbrace{4}_{n}} \sqrt{\smash[b]{1\! \underbrace{44\cdots4\,}_\text{$n$ times}}}$
First of all you should define a command for the separation symbol, so that you're sure it will be uniform in the whole document.
I propose four different choices, select the one which you like most.
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\SL}{SL}
\begin{document}
\newcommand{\ssep}{\mid}
$\SL(V)=\{\, L\in\GL(V) \ssep \lvert L\rvert=1 \,\}=
\{\, L\colon V\to V \ssep \lvert L\rvert=1 \,\}$
\medskip
\renewcommand{\ssep}{:}
$\SL(V)=\{\, L\in\GL(V) \ssep \lvert L\rvert=1 \,\}=
\{\, L\colon V\to V \ssep \lvert L\rvert=1 \,\}$
\medskip
\renewcommand{\ssep}{\,;\,}
$\SL(V)=\{\, L\in\GL(V) \ssep \lvert L\rvert=1 \,\}=
\{\, L\colon V\to V \ssep \lvert L\rvert=1 \,\}$
\medskip
\renewcommand{\ssep}{;}
$\SL(V)=\{\, L\in\GL(V) \ssep \lvert L\rvert=1 \,\}=
\{\, L\colon V\to V \ssep \lvert L\rvert=1 \,\}$
\end{document}
My choice would be for the colon or the bar.
I would never denote by \lvert L\rvert
the determinant of a matrix, which would avoid problems with two consecutive bars. Using \colon
for the symbol in map denotations prevents confusion if the colon is used.
Best Answer
It's simply
\%
. You can use it in or out of math mode.