Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.
$$6\sqrt{3}+5\times 2\sqrt{3}$$
Multiply $5$ and $2$ to get $10$.
$$6\sqrt{3}+10\sqrt{3}$$
Combine $6\sqrt{3}$ and $10\sqrt{3}$ to get $16\sqrt{3}$.
