The effect of \strut on the vertical spacing under a square root is very severe. I would like the effect to be about 20% of what it is. Otherwise, strut solves a lot of problems.
% without \strut
\noindent \hspace{18pt}\large$\bigg[\hspace{1.4pt}x\hspace{1.4pt}'\hspace{-0.6pt}+\dfrac{\big(\hspace{0.4pt}9\hspace{-0.6pt}-\hspace{-0.6pt}5\hspace{0.4pt}\surd{\hspace{1.0pt}2}\hspace{0.8pt}\big) \hspace{1.2pt}\sqrt{ \hspace{1.2pt}4\hspace{-0.6pt}+\hspace{-0.6pt}2\hspace{0.4pt}\surd{\hspace{1.0pt}2}}}{62}\hspace{0.8pt}\bigg]^{\hspace{0.8pt}2}$
% with \strut
\vspace{6pt}
\noindent \hspace{18pt}$\bigg[\hspace{1.4pt}x\hspace{1.4pt}'\hspace{-0.6pt}+\dfrac{\big(\hspace{0.4pt}9\hspace{-0.6pt}-\hspace{-0.6pt}5\hspace{0.4pt}\surd{\hspace{1.0pt}2}\hspace{0.8pt}\big) \hspace{1.2pt}\sqrt{\strut\hspace{1.2pt}4\hspace{-0.6pt}+\hspace{-0.6pt}2\hspace{0.4pt}\surd{\hspace{1.0pt}2}}}{62}\hspace{0.8pt}\bigg]^{\hspace{0.8pt}2}$

\mathstrut-- that's what it's for. on the other hand, if the situation gets too complicated, the answer by @Ulrike explains what's happening. – barbara beeton Aug 17 '17 at 17:12\delimitershortfallwhere a minuscule adjustment in some formula contents could cause the\left-\rightdelimiters to stretch. As reference, see Automatic size adjustment for nested parentheses. – Werner Aug 17 '17 at 20:39