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

\(4\sqrt{2}+2\sqrt{2}=6\sqrt{2}\text{.}\)

\(\sqrt{63}=\sqrt{9}⋅\sqrt{7}=3\sqrt{7}\text{.}\)

\(-2\sqrt{700}=-2⋅\sqrt{100}⋅\sqrt{7}=-2⋅10⋅\sqrt{7}=-20\sqrt{7}\text{.}\)

\(4\sqrt{12}-5\sqrt{27}=4⋅\sqrt{4}⋅\sqrt{3}-5⋅\sqrt{9}⋅\sqrt{3}\text{.}\)

\(4⋅2⋅\sqrt{3}-5⋅3⋅\sqrt{3}=8\sqrt{3}-15\sqrt{3}=-7\sqrt{3}\text{.}\)

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

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

\(\sqrt{2\frac{2}{25}}=\sqrt{\frac{52}{25}}={\sqrt{52} \over \sqrt{25}}={\sqrt{52} \over 5}=\frac{1}{5}\sqrt{52}=\frac{1}{5}⋅2⋅\sqrt{13}=\frac{2}{5}\sqrt{13}\text{.}\)

\(\sqrt{\frac{1}{44}}={\sqrt{1} \over \sqrt{44}}={1 \over \sqrt{44}}⋅{\sqrt{44} \over \sqrt{44}}={\sqrt{44} \over 44}=\frac{1}{44}\sqrt{44}=\frac{1}{44}⋅2⋅\sqrt{11}=\frac{1}{22}\sqrt{11}\text{.}\)

\(\sqrt{1\frac{2}{3}}=\sqrt{\frac{5}{3}}={\sqrt{5} \over \sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={\sqrt{15} \over 3}=\frac{1}{3}\sqrt{15}\text{.}\)

\({21\sqrt{56} \over 3\sqrt{7}}={21 \over 3}⋅{\sqrt{56} \over \sqrt{7}}=7\sqrt{8}=7⋅\sqrt{4}⋅\sqrt{2}=7⋅2⋅\sqrt{2}=14\sqrt{2}\)

\(2\sqrt{15}⋅3\sqrt{3}=6\sqrt{45}=6⋅\sqrt{9}⋅\sqrt{5}=6⋅3⋅\sqrt{5}=18\sqrt{5}\)