`\sqrt{frac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}}`
`=\sqrt{frac{(2\sqrt{10}-2\sqrt{2})+(\sqrt{30}-\sqrt{6})}{2\sqrt{2}(\sqrt{5}-1)}}`
`=\sqrt{frac{2\sqrt{2}(\sqrt{5}-1)+\sqrt{6}(\sqrt{5}-1)}{2\sqrt{2}(\sqrt{5}-1)}}`
`=\sqrt{frac{(2\sqrt{2}+\sqrt{6})(\sqrt{5}-1)}{2\sqrt{2}(\sqrt{5}-1)}}`
`=\sqrt{frac{\sqrt{2}(2+\sqrt{3})(\sqrt{5}-1)}{2\sqrt{2}(\sqrt{5}-1)}}`
`=\sqrt{frac{2+\sqrt{3}}{2}}`
`=\sqrt{frac{2(2+\sqrt{3})}{2.2}}`
`=\sqrt{frac{4+2\sqrt{3}}{4}}`
`=frac{\sqrt{4+2\sqrt{3}}}{\sqrt{4}}`
`=frac{\sqrt{(\sqrt{3}+1)^2}}{2}`
`=frac{\sqrt{3}+1}{2}` (do `\sqrt{3}+1>0)`
