Write in ascending order the numbers

$$
\sqrt{121}, \quad \sqrt[3]{729} \quad \text { and } \quad \sqrt[4]{38416}
$$
Factoring the numbers and extracting the roots, we obtain

$$
\begin{aligned}
& \sqrt{121}=\sqrt{11^{2}}=11 \\
& \sqrt[3]{729}=\sqrt[3]{9^{3}} \quad=9 \text{ and } \\
& \sqrt[4]{38416}=\sqrt[4]{2^{4} \times 7^{4}}=2 \times 7=14
\end{aligned}
$$

Therefore, in ascending order, we have $\sqrt[3]{729}, \sqrt{121}$, and $\sqrt[4]{38416}$.