` a) ` ` A = \sqrt{6 - 2\sqrt{5}} + \sqrt{14 - 6\sqrt{5}} `
` = \sqrt{6 - 2.\sqrt{5}.1} + \sqrt{14 - 2.\sqrt{5}.3} `
` = \sqrt{5 - 2.\sqrt{5}.1 + 1} + \sqrt{5 - 2.\sqrt{5}.3 + 9} `
` = \sqrt{(\sqrt{5} - 1)^2} + \sqrt{(\sqrt{5} - 3)^2} `
` = |\sqrt{5} - 1| + |\sqrt{5} - 3| `
` = \sqrt{5} - 1 + 3 - \sqrt{5} `
` = 2 `
` b) ` ` A = \sqrt{127 - 48\sqrt{7}} - \sqrt{127 + 48\sqrt{7}} `
` = \sqrt{127 - 2.3\sqrt{7}.8} - \sqrt{127 + 2.3\sqrt{7}.8} `
` = \sqrt{63 - 2.3\sqrt{7}.8 + 64} - \sqrt{63 + 2.3\sqrt{7}.8 + 64} `
` = \sqrt{(3\sqrt{7} - 8)^2} - \sqrt{(3\sqrt{7} + 8)^2} `
` = |3\sqrt{7} - 8| - (3\sqrt{7} + 8) `
` = 8 - 3\sqrt{7} - 3\sqrt{7} - 8 `
` = -6\sqrt{7} `
