`A = (2sqrt{4+sqrt{6-2sqrt5}})(sqrt{10}-sqrt2)`
`= (2sqrt{4+sqrt{(sqrt1)^2-2*1sqrt5+(sqrt5)^2}})(sqrt{10}-sqrt2)`
`= (2sqrt{4+sqrt{(1-sqrt5)^2}})(sqrt{10}-sqrt2)`
`= (2sqrt{4+sqrt5-1})(sqrt{10}-sqrt2)`
`= 2sqrt{3+sqrt5}(sqrt{10}-sqrt2)`
`= 2sqrt{30+10sqrt5} - 2sqrt{6+2sqrt5}`
`= 2sqrt{5^2+2*5*sqrt5+(sqrt5)^2} - 2sqrt{(sqrt1)^2+2*1sqrt5+(sqrt5)^2}`
`= 2sqrt{(5+sqrt5)^2} - 2sqrt{(1+sqrt5)^2}`
`= 2(5+sqrt5)-2(1+sqrt5)`
`= 10 + 2sqrt5 - 2 - 2sqrt5`
`= 8`
