Encasing the argument of \sqrt macro in a \smash[b]{...} macro gets the stated job done.
In addition, I think it's important to make sure that the three underbraces are all at the same depth. This may achieved by inserting \vphantom{y} in the xx and zz groups.
For the finishing touch, I'd extend the square root's horizontal bar ever so slightly before \overline{xx...x} and beyond \overline{yy...y}, and I'd place empty "math atoms" around the - and = symbols to improve the horizontal spacing. (For some reason, the presence of the \underbraces interferes with the normal spacing around objects of type mathbin (-) and mathrel (=).)

\documentclass{article}
\usepackage{amsmath} % for '\smash[b]' macro
\setlength\textwidth{2in} % just for this example
\begin{document}
\noindent
some text before \dots % filler text
\[
\sqrt{\smash[b]{\,
\underbrace{\overline{\vphantom{y}xx\cdots x}}_{2n}
{}-{}
\underbrace{\overline{yy\cdots y}}_{n}}\,}
{}={}
\underbrace{\overline{\vphantom{y}zz\cdots z}}_{n}
\]
some text after \dots % filler text
\end{document}