\(\sqrt{45}=\sqrt{9}⋅\sqrt{5}=3\sqrt{5}\text{.}\)

\(3\sqrt{125}=3⋅\sqrt{25}⋅\sqrt{5}=3⋅5⋅\sqrt{5}=15\sqrt{5}\text{.}\)

\(\sqrt{\frac{9}{49}}={\sqrt{9} \over \sqrt{49}}=\frac{3}{7}\text{.}\)

\({27\sqrt{120} \over 9\sqrt{6}}={27 \over 9}⋅{\sqrt{120} \over \sqrt{6}}=3\sqrt{20}=3⋅\sqrt{4}⋅\sqrt{5}=3⋅2⋅\sqrt{5}=6\sqrt{5}\)

\(\sqrt{\frac{67}{100}}={\sqrt{67} \over \sqrt{100}}={\sqrt{67} \over 10}=\frac{1}{10}\sqrt{67}\text{.}\)

\(\sqrt{80}+\sqrt{45}=\sqrt{16}⋅\sqrt{5}+\sqrt{9}⋅\sqrt{5}=4\sqrt{5}+3\sqrt{5}\text{.}\)

\(4\sqrt{5}+3\sqrt{5}=7\sqrt{5}\text{.}\)

\(5\sqrt{8}+4\sqrt{32}=5⋅\sqrt{4}⋅\sqrt{2}+4⋅\sqrt{16}⋅\sqrt{2}\text{.}\)

\(5⋅2⋅\sqrt{2}+4⋅4⋅\sqrt{2}=10\sqrt{2}+16\sqrt{2}=26\sqrt{2}\text{.}\)

\({2 \over 7\sqrt{7}}={2 \over 7\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={2\sqrt{7} \over 7⋅7}=\frac{2}{49}\sqrt{7}\text{.}\)

\(\sqrt{\frac{49}{54}}={\sqrt{49} \over \sqrt{54}}={7 \over \sqrt{54}}⋅{\sqrt{54} \over \sqrt{54}}={7\sqrt{54} \over 54}=\frac{7}{54}\sqrt{54}=\frac{7}{54}⋅3⋅\sqrt{6}=\frac{7}{18}\sqrt{6}\text{.}\)

\(\sqrt{2\frac{4}{5}}=\sqrt{\frac{14}{5}}={\sqrt{14} \over \sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={\sqrt{70} \over 5}=\frac{1}{5}\sqrt{70}\text{.}\)