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 $3^{2}$.
$$3\sqrt{5}+3\sqrt{20}-8\sqrt{5}$$
Factor $20=2^{2}\times 5$. Rewrite the square root of the product $\sqrt{2^{2}\times 5}$ as the product of square roots $\sqrt{2^{2}}\sqrt{5}$. Take the square root of $2^{2}$.
$$3\sqrt{5}+3\times 2\sqrt{5}-8\sqrt{5}$$
Multiply $3$ and $2$ to get $6$.
$$3\sqrt{5}+6\sqrt{5}-8\sqrt{5}$$
Combine $3\sqrt{5}$ and $6\sqrt{5}$ to get $9\sqrt{5}$.
$$9\sqrt{5}-8\sqrt{5}$$
Combine $9\sqrt{5}$ and $-8\sqrt{5}$ to get $\sqrt{5}$.
