\(\sqrt{80} = \sqrt{16} ⋅ \sqrt{5} = 4 \sqrt{5} \text{.}\)

\(3 \sqrt{500} = 3 ⋅ \sqrt{100} ⋅ \sqrt{5} = 3 ⋅ 10 ⋅ \sqrt{5} = 30 \sqrt{5} \text{.}\)

\(\sqrt{\frac{1}{36}} = {\sqrt{1} \over \sqrt{36}} = \frac{1}{6} \text{.}\)

\({16 \sqrt{72} \over 8 \sqrt{3}} = {16 \over 8} ⋅ {\sqrt{72} \over \sqrt{3}} = 2 \sqrt{24} = 2 ⋅ \sqrt{4} ⋅ \sqrt{6} = 2 ⋅ 2 ⋅ \sqrt{6} = 4 \sqrt{6}\)

\(\sqrt{\frac{3}{4}} = {\sqrt{3} \over \sqrt{4}} = {\sqrt{3} \over 2} = \frac{1}{2} \sqrt{3} \text{.}\)