\(\sqrt{20} = \sqrt{4} ⋅ \sqrt{5} = 2 \sqrt{5} \text{.}\)

\(-6 \sqrt{112} = -6 ⋅ \sqrt{16} ⋅ \sqrt{7} = -6 ⋅ 4 ⋅ \sqrt{7} = -24 \sqrt{7} \text{.}\)

\(\sqrt{1\frac{11}{25}} = \sqrt{\frac{36}{25}} = {\sqrt{36} \over \sqrt{25}} = \frac{6}{5} = 1\frac{1}{5} \text{.}\)

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

\(\sqrt{1\frac{46}{49}} = \sqrt{\frac{95}{49}} = {\sqrt{95} \over \sqrt{49}} = {\sqrt{95} \over 7} = \frac{1}{7} \sqrt{95} \text{.}\)