`1)`
`A = 3\sqrt{8} - \sqrt{50} - \sqrt{(\sqrt{2}-1)^2}`
`= 6\sqrt{2} - \sqrt{50} - \sqrt{(\sqrt{2}-1)^2}`
`= 6\sqrt{2} - 5\sqrt{2} - \sqrt{(\sqrt{2}-1)^2}`
`= 6\sqrt{2} - 5\sqrt{2} - 1`
`= \sqrt{2} - 1`
`2)`
`A =\sqrt{50} - 3\sqrt{8} + \sqrt{(\sqrt{2}-1)^2}`
`= 5\sqrt{2} - 6\sqrt{2} - 1`
`= -\sqrt{2} - 1`
`3)`
`A = \sqrt{9-4\sqrt{5}} - \sqrt{5}`
`= \sqrt{5} - 2 \sqrt{5}`
`= - 2`
`4)`
`A = \sqrt{7-4\sqrt{3}} + \sqrt{12+6\sqrt{3}}`
`= 2 - \sqrt{3} + \sqrt{3} + 3`
`= 2 + 3`
`= 5`
`5)`
`A = ( \sqrt{\sqrt{5}+3} - \sqrt{3-\sqrt{5} )^2`
`= (\sqrt{\sqrt{5}+3})^2 - 2\sqrt{\sqrt{5}+3}\sqrt{3-\sqrt{5}}+(\sqrt{3-\sqrt{5}})^2`
`= 2`
`6)`
`A = (\sqrt{6} - \sqrt{2})sqrt{2+\sqrt{3}}`
`= \sqrt{2+\sqrt{3}}\sqrt{6}-\sqrt{2+\sqrt{3}}\sqrt{2}`
`= \sqrt{6}\sqrt{2+\sqrt{3}} - \sqrt{2}\sqrt{2+\sqrt{3}}`
`= 2`
