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 $2^{2}$.
$$2\sqrt{2}-\sqrt{18}+\sqrt{72}$$
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 $3^{2}$.
$$2\sqrt{2}-3\sqrt{2}+\sqrt{72}$$
Combine $2\sqrt{2}$ and $-3\sqrt{2}$ to get $-\sqrt{2}$.
$$-\sqrt{2}+\sqrt{72}$$
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 $6^{2}$.
$$-\sqrt{2}+6\sqrt{2}$$
Combine $-\sqrt{2}$ and $6\sqrt{2}$ to get $5\sqrt{2}$.
