13.42 The largest of the following numbers is
(A) $\sqrt{\sqrt[3]{5 \cdot 6}}$.
(B) $\sqrt{6 \sqrt[3]{5}}$.
(C) $\sqrt{5 \sqrt[3]{6}}$.
(D) $\sqrt[3]{5 \sqrt{6}}$.
(E) $\sqrt[3]{6 \sqrt{5}}$.
(41st American High School Mathematics Examination, 1990)
[Solution] Clearly, $\sqrt{6 \sqrt[3]{5}}>\sqrt{5 \sqrt[3]{6}}>\sqrt{\sqrt[3]{5 \cdot 6}}$.
Also, $\quad \sqrt[3]{6 \sqrt{5}}>\sqrt[3]{5 \sqrt{6}}$,
and
$$
\begin{aligned}
\sqrt{6 \sqrt[3]{5}} & =\sqrt{\sqrt[3]{6^{3} \cdot 5}}=\sqrt[6]{6^{3} \cdot 5}, \sqrt[3]{6 \sqrt{5}} \\
& =\sqrt[3]{\sqrt{6^{2} \cdot 5}}=\sqrt[6]{6^{2} \cdot 5},
\end{aligned}
$$
$\therefore \sqrt{6 \sqrt[3]{5}}>\sqrt[3]{6 \sqrt{5}}$, i.e., (B) is the largest, so the answer is $(B)$.