
\begin{enumerate}
\item $\sqrt{392}=\sqrt{2^2\times7^2\times2}=2\times7\times\sqrt2=\underline{14\sqrt2}$.

\item $\sqrt{\numprint{4608}}=\sqrt{2^9\times3^2}=\sqrt{2^8\times3^2\times2^1}=2^4\times3\times\sqrt2=\underline{48\sqrt2}$.

\item $\sqrt{\numprint{8820}}=\sqrt{2^2\times3^2\times7^2\times5}=2\times3\times7\times\sqrt5=\underline{42\sqrt5}$.

\item $\sqrt{\numprint{111132}}=\sqrt{2^2\times3^4\times7^3}=2\times3^2\times7\sqrt7=\underline{126\sqrt7}$.

\item $\sqrt{\numprint{6272}}=\sqrt{2^7\times7^2}=2^3\times7\sqrt2=\underline{56\sqrt2}$.

\item $\sqrt{\numprint{13552}}=\sqrt{2^4\times7\times11^2}=2^2\times11\sqrt7=\underline{44\sqrt7}$.

\item $\sqrt{\numprint{5010005}}=\sqrt{5\times7^2\times11^2\times13^2}=7\times11\times13\sqrt5=\underline{\numprint{1001}\sqrt5}$.

\item $\sqrt{\numprint{27783}}=\sqrt{3^4\times7^3}=3^2\times7\sqrt7=\underline{63\sqrt7}$.

\item $\sqrt{\numprint{226800}}=\sqrt{2^4\times3^4\times5^2\times7}=2^2\times3^2\times5\sqrt7=\underline{180\sqrt7}$.
\end{enumerate}
