\(\sqrt{200}+\sqrt{8}=\sqrt{100}⋅\sqrt{2}+\sqrt{4}⋅\sqrt{2}=10\sqrt{2}+2\sqrt{2}\text{.}\)

\(10\sqrt{2}+2\sqrt{2}=12\sqrt{2}\text{.}\)

\(\sqrt{18}=\sqrt{9}⋅\sqrt{2}=3\sqrt{2}\text{.}\)

\(6\sqrt{8}=6⋅\sqrt{4}⋅\sqrt{2}=6⋅2⋅\sqrt{2}=12\sqrt{2}\text{.}\)

\(3\sqrt{18}+5\sqrt{32}=3⋅\sqrt{9}⋅\sqrt{2}+5⋅\sqrt{16}⋅\sqrt{2}\text{.}\)

\(3⋅3⋅\sqrt{2}+5⋅4⋅\sqrt{2}=9\sqrt{2}+20\sqrt{2}=29\sqrt{2}\text{.}\)

\(\sqrt{\frac{4}{49}}={\sqrt{4} \over \sqrt{49}}=\frac{2}{7}\text{.}\)

\({2 \over 9\sqrt{7}}={2 \over 9\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={2\sqrt{7} \over 9⋅7}=\frac{2}{63}\sqrt{7}\text{.}\)

\(\sqrt{4\frac{1}{16}}=\sqrt{\frac{65}{16}}={\sqrt{65} \over \sqrt{16}}={\sqrt{65} \over 4}=\frac{1}{4}\sqrt{65}\text{.}\)

\(\sqrt{\frac{9}{41}}={\sqrt{9} \over \sqrt{41}}={3 \over \sqrt{41}}⋅{\sqrt{41} \over \sqrt{41}}={3\sqrt{41} \over 41}=\frac{3}{41}\sqrt{41}\text{.}\)

\(\sqrt{6\frac{2}{3}}=\sqrt{\frac{20}{3}}={\sqrt{20} \over \sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={\sqrt{60} \over 3}=\frac{1}{3}\sqrt{60}=\frac{1}{3}⋅2⋅\sqrt{15}=\frac{2}{3}\sqrt{15}\text{.}\)

\({42\sqrt{72} \over 6\sqrt{3}}={42 \over 6}⋅{\sqrt{72} \over \sqrt{3}}=7\sqrt{24}=7⋅\sqrt{4}⋅\sqrt{6}=7⋅2⋅\sqrt{6}=14\sqrt{6}\)

\(3\sqrt{14}⋅4\sqrt{7}=12\sqrt{98}=12⋅\sqrt{49}⋅\sqrt{2}=12⋅7⋅\sqrt{2}=84\sqrt{2}\)