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 $4^{2}$.
$$\beta =3+4\sqrt{5}-\sqrt{9}-\sqrt{80}$$
Calculate the square root of $9$ and get $3$.
$$\beta =3+4\sqrt{5}-3-\sqrt{80}$$
Subtract $3$ from $3$ to get $0$.
$$\beta =4\sqrt{5}-\sqrt{80}$$
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 $4^{2}$.
