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

\(6 \sqrt{45} = 6 ⋅ \sqrt{9} ⋅ \sqrt{5} = 6 ⋅ 3 ⋅ \sqrt{5} = 18 \sqrt{5} \text{.}\)

\(\sqrt{2\frac{7}{9}} = \sqrt{\frac{25}{9}} = {\sqrt{25} \over \sqrt{9}} = \frac{5}{3} = 1\frac{2}{3} \text{.}\)

\({45 \sqrt{96} \over 5 \sqrt{8}} = {45 \over 5} ⋅ {\sqrt{96} \over \sqrt{8}} = 9 \sqrt{12} = 9 ⋅ \sqrt{4} ⋅ \sqrt{3} = 9 ⋅ 2 ⋅ \sqrt{3} = 18 \sqrt{3}\)

\(\sqrt{\frac{5}{81}} = {\sqrt{5} \over \sqrt{81}} = {\sqrt{5} \over 9} = \frac{1}{9} \sqrt{5} \text{.}\)