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

\(-6 \sqrt{500} = -6 ⋅ \sqrt{100} ⋅ \sqrt{5} = -6 ⋅ 10 ⋅ \sqrt{5} = -60 \sqrt{5} \text{.}\)

\(\sqrt{\frac{9}{64}} = {\sqrt{9} \over \sqrt{64}} = \frac{3}{8} \text{.}\)

\({18 \sqrt{240} \over 3 \sqrt{6}} = {18 \over 3} ⋅ {\sqrt{240} \over \sqrt{6}} = 6 \sqrt{40} = 6 ⋅ \sqrt{4} ⋅ \sqrt{10} = 6 ⋅ 2 ⋅ \sqrt{10} = 12 \sqrt{10}\)

\(\sqrt{1\frac{41}{49}} = \sqrt{\frac{90}{49}} = {\sqrt{90} \over \sqrt{49}} = {\sqrt{90} \over 7} = \frac{1}{7} \sqrt{90} = \frac{1}{7} ⋅ 3 ⋅ \sqrt{10} = \frac{3}{7} \sqrt{10} \text{.}\)