Factor $117=3^{2}\times 13$. Rewrite the square root of the product $\sqrt{3^{2}\times 13}$ as the product of square roots $\sqrt{3^{2}}\sqrt{13}$. Take the square root of $3^{2}$.
$$3\sqrt{13}\sqrt{396}$$
Factor $396=6^{2}\times 11$. Rewrite the square root of the product $\sqrt{6^{2}\times 11}$ as the product of square roots $\sqrt{6^{2}}\sqrt{11}$. Take the square root of $6^{2}$.
$$3\sqrt{13}\times 6\sqrt{11}$$
Multiply $3$ and $6$ to get $18$.
$$18\sqrt{13}\sqrt{11}$$
To multiply $\sqrt{13}$ and $\sqrt{11}$, multiply the numbers under the square root.
