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 $4^{2}$.
$$4\sqrt{5}-2\sqrt{252}+3\sqrt{405}$$
Factor $252=6^{2}\times 7$. Rewrite the square root of the product $\sqrt{6^{2}\times 7}$ as the product of square roots $\sqrt{6^{2}}\sqrt{7}$. Take the square root of $6^{2}$.
$$4\sqrt{5}-2\times 6\sqrt{7}+3\sqrt{405}$$
Multiply $-2$ and $6$ to get $-12$.
$$4\sqrt{5}-12\sqrt{7}+3\sqrt{405}$$
Factor $405=9^{2}\times 5$. Rewrite the square root of the product $\sqrt{9^{2}\times 5}$ as the product of square roots $\sqrt{9^{2}}\sqrt{5}$. Take the square root of $9^{2}$.
$$4\sqrt{5}-12\sqrt{7}+3\times 9\sqrt{5}$$
Multiply $3$ and $9$ to get $27$.
$$4\sqrt{5}-12\sqrt{7}+27\sqrt{5}$$
Combine $4\sqrt{5}$ and $27\sqrt{5}$ to get $31\sqrt{5}$.
