\(\sqrt{300}=\sqrt{100}⋅\sqrt{3}=10\sqrt{3}\text{.}\)

\(3\sqrt{700}=3⋅\sqrt{100}⋅\sqrt{7}=3⋅10⋅\sqrt{7}=30\sqrt{7}\text{.}\)

\(\sqrt{\frac{4}{25}}={\sqrt{4} \over \sqrt{25}}=\frac{2}{5}\text{.}\)

\(\sqrt{1\frac{7}{81}}=\sqrt{\frac{88}{81}}={\sqrt{88} \over \sqrt{81}}={\sqrt{88} \over 9}=\frac{1}{9}\sqrt{88}=\frac{1}{9}⋅2⋅\sqrt{22}=\frac{2}{9}\sqrt{22}\text{.}\)

\(\sqrt{12}+\sqrt{27}=\sqrt{4}⋅\sqrt{3}+\sqrt{9}⋅\sqrt{3}=2\sqrt{3}+3\sqrt{3}\text{.}\)

\(2\sqrt{3}+3\sqrt{3}=5\sqrt{3}\text{.}\)

\(4\sqrt{75}+2\sqrt{12}=4⋅\sqrt{25}⋅\sqrt{3}+2⋅\sqrt{4}⋅\sqrt{3}\text{.}\)

\(4⋅5⋅\sqrt{3}+2⋅2⋅\sqrt{3}=20\sqrt{3}+4\sqrt{3}=24\sqrt{3}\text{.}\)

\({2 \over 7\sqrt{5}}={2 \over 7\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={2\sqrt{5} \over 7⋅5}=\frac{2}{35}\sqrt{5}\text{.}\)

\(\sqrt{1\frac{12}{13}}=\sqrt{\frac{25}{13}}={\sqrt{25} \over \sqrt{13}}={5 \over \sqrt{13}}⋅{\sqrt{13} \over \sqrt{13}}={5\sqrt{13} \over 13}=\frac{5}{13}\sqrt{13}\text{.}\)

\(\sqrt{\frac{5}{18}}={\sqrt{5} \over \sqrt{18}}⋅{\sqrt{18} \over \sqrt{18}}={\sqrt{90} \over 18}=\frac{1}{18}\sqrt{90}=\frac{1}{18}⋅3⋅\sqrt{10}=\frac{1}{6}\sqrt{10}\text{.}\)