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

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

\(\sqrt{\frac{16}{81}} = {\sqrt{16} \over \sqrt{81}} = \frac{4}{9} \text{.}\)

\({18 \sqrt{24} \over 3 \sqrt{2}} = {18 \over 3} ⋅ {\sqrt{24} \over \sqrt{2}} = 6 \sqrt{12} = 6 ⋅ \sqrt{4} ⋅ \sqrt{3} = 6 ⋅ 2 ⋅ \sqrt{3} = 12 \sqrt{3}\)

\(\sqrt{\frac{8}{25}} = {\sqrt{8} \over \sqrt{25}} = {\sqrt{8} \over 5} = \frac{1}{5} \sqrt{8} = \frac{1}{5} ⋅ 2 ⋅ \sqrt{2} = \frac{2}{5} \sqrt{2} \text{.}\)