\(\sqrt{125}+\sqrt{20}=\sqrt{25}⋅\sqrt{5}+\sqrt{4}⋅\sqrt{5}=5\sqrt{5}+2\sqrt{5}\text{.}\)

\(5\sqrt{5}+2\sqrt{5}=7\sqrt{5}\text{.}\)

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

\(6\sqrt{32}=6⋅\sqrt{16}⋅\sqrt{2}=6⋅4⋅\sqrt{2}=24\sqrt{2}\text{.}\)

\(6\sqrt{50}-4\sqrt{32}=6⋅\sqrt{25}⋅\sqrt{2}-4⋅\sqrt{16}⋅\sqrt{2}\text{.}\)

\(6⋅5⋅\sqrt{2}-4⋅4⋅\sqrt{2}=30\sqrt{2}-16\sqrt{2}=14\sqrt{2}\text{.}\)

\(\sqrt{1\frac{24}{25}}=\sqrt{\frac{49}{25}}={\sqrt{49} \over \sqrt{25}}=\frac{7}{5}=1\frac{2}{5}\text{.}\)

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

\(\sqrt{\frac{44}{81}}={\sqrt{44} \over \sqrt{81}}={\sqrt{44} \over 9}=\frac{1}{9}\sqrt{44}=\frac{1}{9}⋅2⋅\sqrt{11}=\frac{2}{9}\sqrt{11}\text{.}\)

\(\sqrt{1\frac{27}{37}}=\sqrt{\frac{64}{37}}={\sqrt{64} \over \sqrt{37}}={8 \over \sqrt{37}}⋅{\sqrt{37} \over \sqrt{37}}={8\sqrt{37} \over 37}=\frac{8}{37}\sqrt{37}\text{.}\)

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

\({72\sqrt{72} \over 9\sqrt{3}}={72 \over 9}⋅{\sqrt{72} \over \sqrt{3}}=8\sqrt{24}=8⋅\sqrt{4}⋅\sqrt{6}=8⋅2⋅\sqrt{6}=16\sqrt{6}\)

\(3\sqrt{6}⋅5\sqrt{10}=15\sqrt{60}=15⋅\sqrt{4}⋅\sqrt{15}=15⋅2⋅\sqrt{15}=30\sqrt{15}\)