\(\sqrt{500}+\sqrt{45}=\sqrt{100}⋅\sqrt{5}+\sqrt{9}⋅\sqrt{5}=10\sqrt{5}+3\sqrt{5}\text{.}\)

\(10\sqrt{5}+3\sqrt{5}=13\sqrt{5}\text{.}\)

\(\sqrt{28}=\sqrt{4}⋅\sqrt{7}=2\sqrt{7}\text{.}\)

\(7\sqrt{48}=7⋅\sqrt{16}⋅\sqrt{3}=7⋅4⋅\sqrt{3}=28\sqrt{3}\text{.}\)

\(4\sqrt{32}-3\sqrt{50}=4⋅\sqrt{16}⋅\sqrt{2}-3⋅\sqrt{25}⋅\sqrt{2}\text{.}\)

\(4⋅4⋅\sqrt{2}-3⋅5⋅\sqrt{2}=16\sqrt{2}-15\sqrt{2}=1\sqrt{2}\text{.}\)

\(\sqrt{1\frac{9}{16}}=\sqrt{\frac{25}{16}}={\sqrt{25} \over \sqrt{16}}=\frac{5}{4}=1\frac{1}{4}\text{.}\)

\({9 \over 4\sqrt{5}}={9 \over 4\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={9\sqrt{5} \over 4⋅5}=\frac{9}{20}\sqrt{5}\text{.}\)

\(\sqrt{3\frac{22}{25}}=\sqrt{\frac{97}{25}}={\sqrt{97} \over \sqrt{25}}={\sqrt{97} \over 5}=\frac{1}{5}\sqrt{97}\text{.}\)

\(\sqrt{\frac{1}{60}}={\sqrt{1} \over \sqrt{60}}={1 \over \sqrt{60}}⋅{\sqrt{60} \over \sqrt{60}}={\sqrt{60} \over 60}=\frac{1}{60}\sqrt{60}=\frac{1}{60}⋅2⋅\sqrt{15}=\frac{1}{30}\sqrt{15}\text{.}\)

\(\sqrt{\frac{3}{32}}={\sqrt{3} \over \sqrt{32}}⋅{\sqrt{32} \over \sqrt{32}}={\sqrt{96} \over 32}=\frac{1}{32}\sqrt{96}=\frac{1}{32}⋅4⋅\sqrt{6}=\frac{1}{8}\sqrt{6}\text{.}\)

\({9\sqrt{84} \over \sqrt{7}}=9⋅{\sqrt{84} \over \sqrt{7}}=9\sqrt{12}=9⋅\sqrt{4}⋅\sqrt{3}=9⋅2⋅\sqrt{3}=18\sqrt{3}\)

\(5\sqrt{5}⋅4\sqrt{10}=20\sqrt{50}=20⋅\sqrt{25}⋅\sqrt{2}=20⋅5⋅\sqrt{2}=100\sqrt{2}\)