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

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

\(\sqrt{1\frac{15}{49}}=\sqrt{\frac{64}{49}}={\sqrt{64} \over \sqrt{49}}=\frac{8}{7}=1\frac{1}{7}\text{.}\)

\({12\sqrt{192} \over 4\sqrt{8}}={12 \over 4}⋅{\sqrt{192} \over \sqrt{8}}=3\sqrt{24}=3⋅\sqrt{4}⋅\sqrt{6}=3⋅2⋅\sqrt{6}=6\sqrt{6}\)

\(\sqrt{1\frac{13}{81}}=\sqrt{\frac{94}{81}}={\sqrt{94} \over \sqrt{81}}={\sqrt{94} \over 9}=\frac{1}{9}\sqrt{94}\text{.}\)

\(\sqrt{27}+\sqrt{75}=\sqrt{9}⋅\sqrt{3}+\sqrt{25}⋅\sqrt{3}=3\sqrt{3}+5\sqrt{3}\text{.}\)

\(3\sqrt{3}+5\sqrt{3}=8\sqrt{3}\text{.}\)

\(3\sqrt{27}-7\sqrt{300}=3⋅\sqrt{9}⋅\sqrt{3}-7⋅\sqrt{100}⋅\sqrt{3}\text{.}\)

\(3⋅3⋅\sqrt{3}-7⋅10⋅\sqrt{3}=9\sqrt{3}-70\sqrt{3}=-61\sqrt{3}\text{.}\)

\({5 \over 4\sqrt{5}}={5 \over 4\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={5\sqrt{5} \over 4⋅5}=\frac{1}{4}\sqrt{5}\text{.}\)

\(\sqrt{1\frac{28}{53}}=\sqrt{\frac{81}{53}}={\sqrt{81} \over \sqrt{53}}={9 \over \sqrt{53}}⋅{\sqrt{53} \over \sqrt{53}}={9\sqrt{53} \over 53}=\frac{9}{53}\sqrt{53}\text{.}\)

\(\sqrt{\frac{3}{20}}={\sqrt{3} \over \sqrt{20}}⋅{\sqrt{20} \over \sqrt{20}}={\sqrt{60} \over 20}=\frac{1}{20}\sqrt{60}=\frac{1}{20}⋅2⋅\sqrt{15}=\frac{1}{10}\sqrt{15}\text{.}\)

\(2\sqrt{14}⋅3\sqrt{6}=6\sqrt{84}=6⋅\sqrt{4}⋅\sqrt{21}=6⋅2⋅\sqrt{21}=12\sqrt{21}\)