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 \vphantomoutside 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:
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.