\(\sqrt{175} = \sqrt{25} ⋅ \sqrt{7} = 5 \sqrt{7} \text{.}\)

\(-4 \sqrt{27} = -4 ⋅ \sqrt{9} ⋅ \sqrt{3} = -4 ⋅ 3 ⋅ \sqrt{3} = -12 \sqrt{3} \text{.}\)

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

\({35 \sqrt{280} \over 5 \sqrt{7}} = {35 \over 5} ⋅ {\sqrt{280} \over \sqrt{7}} = 7 \sqrt{40} = 7 ⋅ \sqrt{4} ⋅ \sqrt{10} = 7 ⋅ 2 ⋅ \sqrt{10} = 14 \sqrt{10}\)