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 $2^{2}$.
$$3\sqrt{5}+2\times 2\sqrt{5}+\sqrt{45}$$
Multiply $2$ and $2$ to get $4$.
$$3\sqrt{5}+4\sqrt{5}+\sqrt{45}$$
Combine $3\sqrt{5}$ and $4\sqrt{5}$ to get $7\sqrt{5}$.
$$7\sqrt{5}+\sqrt{45}$$
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 $3^{2}$.
$$7\sqrt{5}+3\sqrt{5}$$
Combine $7\sqrt{5}$ and $3\sqrt{5}$ to get $10\sqrt{5}$.
