\(\sqrt{125}+\sqrt{80}=\sqrt{25}⋅\sqrt{5}+\sqrt{16}⋅\sqrt{5}=5\sqrt{5}+4\sqrt{5}\text{.}\)

\(5\sqrt{5}+4\sqrt{5}=9\sqrt{5}\text{.}\)

\(\sqrt{8}=\sqrt{4}⋅\sqrt{2}=2\sqrt{2}\text{.}\)

\(-3\sqrt{18}=-3⋅\sqrt{9}⋅\sqrt{2}=-3⋅3⋅\sqrt{2}=-9\sqrt{2}\text{.}\)

\(7\sqrt{125}-4\sqrt{500}=7⋅\sqrt{25}⋅\sqrt{5}-4⋅\sqrt{100}⋅\sqrt{5}\text{.}\)

\(7⋅5⋅\sqrt{5}-4⋅10⋅\sqrt{5}=35\sqrt{5}-40\sqrt{5}=-5\sqrt{5}\text{.}\)

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

\({5 \over 8\sqrt{7}}={5 \over 8\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={5\sqrt{7} \over 8⋅7}=\frac{5}{56}\sqrt{7}\text{.}\)

\(\sqrt{\frac{28}{81}}={\sqrt{28} \over \sqrt{81}}={\sqrt{28} \over 9}=\frac{1}{9}\sqrt{28}=\frac{1}{9}⋅2⋅\sqrt{7}=\frac{2}{9}\sqrt{7}\text{.}\)

\(\sqrt{1\frac{40}{41}}=\sqrt{\frac{81}{41}}={\sqrt{81} \over \sqrt{41}}={9 \over \sqrt{41}}⋅{\sqrt{41} \over \sqrt{41}}={9\sqrt{41} \over 41}=\frac{9}{41}\sqrt{41}\text{.}\)

\(\sqrt{10\frac{2}{3}}=\sqrt{\frac{32}{3}}={\sqrt{32} \over \sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={\sqrt{96} \over 3}=\frac{1}{3}\sqrt{96}=\frac{1}{3}⋅4⋅\sqrt{6}=1\frac{1}{3}\sqrt{6}\text{.}\)

\({6\sqrt{280} \over 2\sqrt{10}}={6 \over 2}⋅{\sqrt{280} \over \sqrt{10}}=3\sqrt{28}=3⋅\sqrt{4}⋅\sqrt{7}=3⋅2⋅\sqrt{7}=6\sqrt{7}\)

\(4\sqrt{15}⋅5\sqrt{5}=20\sqrt{75}=20⋅\sqrt{25}⋅\sqrt{3}=20⋅5⋅\sqrt{3}=100\sqrt{3}\)