Question

Simplify: $\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$.

Answer 1

$$\begin{gathered} \frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}=\frac{2\sqrt{3\times 3\times 5}+3\sqrt{2\times 2\times 5}}{2\sqrt{5}} \\ =\frac{2\times 3\sqrt{5}+3\times 2\sqrt{5}}{2\sqrt{5}} \\ =\frac{6\sqrt{5}+6\sqrt{5}}{2\sqrt{5}} \\ =\frac{12\sqrt{5}}{2\sqrt{5}} \\ =6 \end{gathered}$$

Hence, simplified form of $\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$ is 6.