Factor $80=4^{2}\times 5$. Rewrite the square root of the product $\sqrt{4^{2}\times 5}$ as the product of square roots $\sqrt{4^{2}}\sqrt{5}$. Take the square root of $4^{2}$.
Factor $180=6^{2}\times 5$. Rewrite the square root of the product $\sqrt{6^{2}\times 5}$ as the product of square roots $\sqrt{6^{2}}\sqrt{5}$. Take the square root of $6^{2}$.
Combine $4\sqrt{5}$ and $6\sqrt{5}$ to get $10\sqrt{5}$.
$$10\sqrt{5}\left(\sqrt{125}-\sqrt{45}\right)$$
Factor $125=5^{2}\times 5$. Rewrite the square root of the product $\sqrt{5^{2}\times 5}$ as the product of square roots $\sqrt{5^{2}}\sqrt{5}$. Take the square root of $5^{2}$.
$$10\sqrt{5}\left(5\sqrt{5}-\sqrt{45}\right)$$
Factor $45=3^{2}\times 5$. Rewrite the square root of the product $\sqrt{3^{2}\times 5}$ as the product of square roots $\sqrt{3^{2}}\sqrt{5}$. Take the square root of $3^{2}$.
$$10\sqrt{5}\left(5\sqrt{5}-3\sqrt{5}\right)$$
Combine $5\sqrt{5}$ and $-3\sqrt{5}$ to get $2\sqrt{5}$.
