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 $2^{2}$.
$$\frac{2\sqrt{5}}{2}+\sqrt{\frac{5}{4}}$$
Cancel out $2$ and $2$.
$$\sqrt{5}+\sqrt{\frac{5}{4}}$$
Rewrite the square root of the division $\sqrt{\frac{5}{4}}$ as the division of square roots $\frac{\sqrt{5}}{\sqrt{4}}$.
$$\sqrt{5}+\frac{\sqrt{5}}{\sqrt{4}}$$
Calculate the square root of $4$ and get $2$.
$$\sqrt{5}+\frac{\sqrt{5}}{2}$$
Combine $\sqrt{5}$ and $\frac{\sqrt{5}}{2}$ to get $\frac{3}{2}\sqrt{5}$.
