Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$2\times 2\sqrt{2}+\sqrt{72}$$
Multiply $2$ and $2$ to get $4$.
$$4\sqrt{2}+\sqrt{72}$$
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 $6^{2}$.
$$4\sqrt{2}+6\sqrt{2}$$
Combine $4\sqrt{2}$ and $6\sqrt{2}$ to get $10\sqrt{2}$.
