Factor $18=3^{2}\times 2$. Rewrite the square root of the product $\sqrt{3^{2}\times 2}$ as the product of square roots $\sqrt{3^{2}}\sqrt{2}$. Take the square root of $3^{2}$.
Factor $24=2^{2}\times 6$. Rewrite the square root of the product $\sqrt{2^{2}\times 6}$ as the product of square roots $\sqrt{2^{2}}\sqrt{6}$. Take the square root of $2^{2}$.
To multiply $\sqrt{39}$ and $\sqrt{6}$, multiply the numbers under the square root.
$$\frac{3\sqrt{2}+6\sqrt{3}+\sqrt{234}}{72}$$
Factor $234=3^{2}\times 26$. Rewrite the square root of the product $\sqrt{3^{2}\times 26}$ as the product of square roots $\sqrt{3^{2}}\sqrt{26}$. Take the square root of $3^{2}$.
