How to maintain the shape of a surd when using enlarged grouping inside the radical?

When this MWE is compiled, the appearance of the surd in equation (1) is correct (the parenthesis are placeholders to demonstrate the issue without using \left( and \right)).

When \left( and \right) is used in equation (2), the surd becomes more vertical, decidedly not what looks best.

The same is true for \big and friends.

% MWE
\documentclass{book}
\usepackage{amsmath}
\begin{document}
\begin{align}
\sqrt{3\sqrt{3}
\left(3+\frac{11}{3}\frac{\sqrt{2}}{\sqrt{3}}\right)}&=
\label{q11401}\\
\sqrt{3\sqrt{3}
(3+\frac{11}{3}\frac{\sqrt{2}}{\sqrt{3}})}&=
\label{q11402}
\end{align}
\end{document} How do I maintain the shape of the surd when using enlarged groupings inside the radical? This should not require a custom macro, should it?

Or did I miss a step?

You could perhaps use lmodern \documentclass{book}
\usepackage{lmodern}
\usepackage{amsmath}
\begin{document}
\begin{align}
\sqrt{3\sqrt{3}
\left(3+\frac{11}{3}\frac{\sqrt{2}}{\sqrt{3}}\right)}&=
\label{q11401}\\
\sqrt{3\sqrt{3}
(3+\frac{11}{3}\frac{\sqrt{2}}{\sqrt{3}})}&=
\label{q11402}
\end{align}
\end{document}

Each font has a fixed number of square root symbols at fixed size and above that will always revert to a vertical form that can be stretched to arbitrary size by inserting a vertical segment, your initial example just happened to be at a critical point for the computer modern font where a small change in size of the argument pushed you past the last "sloped" size,

• you failed to notice that the vertical extent of the enlarged parentheses is apparently what is forcing the edge case. as such, this problem could most likely be solved by using an appropriate size of \big... modifiers. in fact, \biggl ... \biggr does exactly that. – barbara beeton Apr 25 '18 at 17:13
• @barbarabeeton well.. I did notice that but yes if the brackets were smaller it would be like case 2 (where they are smaller in an exaggerated way) but then there wouldn't be a question to answer:-) – David Carlisle Apr 25 '18 at 17:57