`6,` `B = \sqrt{(4-3\sqrt{2})^2} - \sqrt{11+6\sqrt{2}}`

`= | 4 - 3\sqrt{2} | - \sqrt{(3+\sqrt{2})^2}`

`= -4 + 3\sqrt{2} - | 3 + \sqrt{2} |`

`= -4 + 3\sqrt{2} - 3 - \sqrt{2} `

`= 2\sqrt{2} - 7`

`--------`

`7,` `B = (1 - \sqrt{3})^2 - \sqrt{4-2\sqrt{3}} + 3\sqrt{3}`

`= 1 - 2\sqrt{3} + 3 - \sqrt{(\sqrt{3}-1)^2} + 3\sqrt{3}`

`= 1 - 2\sqrt{3} + 3 -  | \sqrt{3}-1 | + 3\sqrt{3}`

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

`= 5`

`--------`

`8,` `B = \sqrt{(\sqrt{3}-2)^2} + \sqrt{19+8\sqrt{3}}`

`= | \sqrt{3}-2 | + \sqrt{(\sqrt{3}+4)^2}`

`= 2 - \sqrt{3} + | \sqrt{3}+4 |`

`= 2 - \sqrt{3} + \sqrt{3}+4`

`= 6`