Prove that `sqrt(" "){8 sqrt3 + sqrt5 + sqrt(" ")(8 -2 sqrt15)}= 3 root(4)(3)`

Explanation

`sqrt(" "){sqrt3 + sqrt5 + sqrt(" ")(8 -2 sqrt15)} = sqrt(" ") { 8 + sqrt3 + sqrt5 + sqrt(" " )(3 + 5 -2 sqrt(3 xx 5))}`
`= sqrt(" ") [8 sqrt3 + sqrt5 + sqrt(" "){(sqrt3)^(2) + (sqrt5)^(2) -2 xx sqrt3 xx sqrt5}]`
`= sqrt(" ")[8sqrt3 + sqrt5 + sqrt(" ")(sqrt3 - sqrt5)^(2)]`
`= sqrt(" ") [8 sqrt3 + sqrt5 + sqrt3 - sqrt5]`
`= sqrt[9 sqrt3] = 3 root(4)(3)`