\(\sqrt{12}=\sqrt{4}⋅\sqrt{3}=2\sqrt{3}\text{.}\)

\(3\sqrt{175}=3⋅\sqrt{25}⋅\sqrt{7}=3⋅5⋅\sqrt{7}=15\sqrt{7}\text{.}\)

\(\sqrt{\frac{1}{9}}={\sqrt{1} \over \sqrt{9}}=\frac{1}{3}\text{.}\)

\({48\sqrt{120} \over 6\sqrt{10}}={48 \over 6}⋅{\sqrt{120} \over \sqrt{10}}=8\sqrt{12}=8⋅\sqrt{4}⋅\sqrt{3}=8⋅2⋅\sqrt{3}=16\sqrt{3}\)

\(\sqrt{3\frac{21}{25}}=\sqrt{\frac{96}{25}}={\sqrt{96} \over \sqrt{25}}={\sqrt{96} \over 5}=\frac{1}{5}\sqrt{96}=\frac{1}{5}⋅4⋅\sqrt{6}=\frac{4}{5}\sqrt{6}\text{.}\)