Factor $72=6^{2}\times 2$. Rewrite the square root of the product $\sqrt{6^{2}\times 2}$ as the product of square roots $\sqrt{6^{2}}\sqrt{2}$. Take the square root of $6^{2}$.
$$5\times 6\sqrt{2}+8\sqrt{72}+9\sqrt{72}$$
Multiply $5$ and $6$ to get $30$.
$$30\sqrt{2}+8\sqrt{72}+9\sqrt{72}$$
Factor $72=6^{2}\times 2$. Rewrite the square root of the product $\sqrt{6^{2}\times 2}$ as the product of square roots $\sqrt{6^{2}}\sqrt{2}$. Take the square root of $6^{2}$.
$$30\sqrt{2}+8\times 6\sqrt{2}+9\sqrt{72}$$
Multiply $8$ and $6$ to get $48$.
$$30\sqrt{2}+48\sqrt{2}+9\sqrt{72}$$
Combine $30\sqrt{2}$ and $48\sqrt{2}$ to get $78\sqrt{2}$.
$$78\sqrt{2}+9\sqrt{72}$$
Factor $72=6^{2}\times 2$. Rewrite the square root of the product $\sqrt{6^{2}\times 2}$ as the product of square roots $\sqrt{6^{2}}\sqrt{2}$. Take the square root of $6^{2}$.
$$78\sqrt{2}+9\times 6\sqrt{2}$$
Multiply $9$ and $6$ to get $54$.
$$78\sqrt{2}+54\sqrt{2}$$
Combine $78\sqrt{2}$ and $54\sqrt{2}$ to get $132\sqrt{2}$.
