$$\sqrt{3\frac{1}{5}}+\sqrt{1\frac{1}{4}}):\frac{5}{\sqrt{180}}=$$
$\frac{13\sqrt{5}}{10}\approx 2.906888371$
$$\sqrt{\frac{15+1}{5}}+\sqrt{\frac{1\times 4+1}{4}}$$
$$\sqrt{\frac{16}{5}}+\sqrt{\frac{1\times 4+1}{4}}$$
$$\frac{\sqrt{16}}{\sqrt{5}}+\sqrt{\frac{1\times 4+1}{4}}$$
$$\frac{4}{\sqrt{5}}+\sqrt{\frac{1\times 4+1}{4}}$$
$$\frac{4\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+\sqrt{\frac{1\times 4+1}{4}}$$
$$\frac{4\sqrt{5}}{5}+\sqrt{\frac{1\times 4+1}{4}}$$
$$\frac{4\sqrt{5}}{5}+\sqrt{\frac{4+1}{4}}$$
$$\frac{4\sqrt{5}}{5}+\sqrt{\frac{5}{4}}$$
$$\frac{4\sqrt{5}}{5}+\frac{\sqrt{5}}{\sqrt{4}}$$
$$\frac{4\sqrt{5}}{5}+\frac{\sqrt{5}}{2}$$
$$\frac{13}{10}\sqrt{5}$$
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