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`a) sqrt{ ( sqrt8 - 4 )^2 } + sqrt8 `

`= | sqrt8 - 4 | + sqrt8 `

`= 4 - sqrt8 + sqrt8 `

`= 4 `

`b) sqrt{9a } - sqrt{ 144a} + sqrt{ 49a} ( a > 0 ) `

`= sqrt{ 3^2 a } - sqrt{ 12^2 a } + sqrt{ 7^2 a } `

`= 3sqrta - 12sqrta + 7sqrta `

`= - 2sqrta `

`c) sqrt{ 4 + 2sqrt3 } - sqrt{ 4 - 2sqrt3 } `

`= sqrt{ 3 + 2sqrt3 + 1 } - sqrt{ 3 - 2sqrt3 + 1 } `

`= sqrt{ ( sqrt3 )^2 + 2 . sqrt3 . 1 + 1^2 } - sqrt{ ( sqrt3 )^2 - 2 . sqrt3 . 1 + 1^2 } `

`= sqrt{ ( sqrt3 + 1 )^2 } - sqrt{ ( sqrt3 - 1 )^2 } `

`= | sqrt3 + 1 | - | sqrt3 - 1 | `

`= sqrt3 + 1 - sqrt3 + 1 `

`= 2 `