\(\sqrt{27}=\sqrt{9}⋅\sqrt{3}=3\sqrt{3}\text{.}\)

\(7\sqrt{175}=7⋅\sqrt{25}⋅\sqrt{7}=7⋅5⋅\sqrt{7}=35\sqrt{7}\text{.}\)

\(\sqrt{11\frac{1}{9}}=\sqrt{\frac{100}{9}}={\sqrt{100} \over \sqrt{9}}=\frac{10}{3}=3\frac{1}{3}\text{.}\)

\({30\sqrt{36} \over 5\sqrt{3}}={30 \over 5}⋅{\sqrt{36} \over \sqrt{3}}=6\sqrt{12}=6⋅\sqrt{4}⋅\sqrt{3}=6⋅2⋅\sqrt{3}=12\sqrt{3}\)

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