Đáp án: + Giải thích các bước giải:
`a) 2\sqrt{5} - \sqrt{125} - \sqrt{80} + \sqrt{605}`
`= 2\sqrt{5} - 5\sqrt{5} - 4\sqrt{5} + 11\sqrt{5}`
`= 4\sqrt{5}`
`b) \sqrt{15-\sqrt{216}} + \sqrt{33-12\sqrt{6}}`
`= 3 - \sqrt{6} + 2\sqrt{6} - 3`
`= 3 + \sqrt{6} - 3`
`= \sqrt{6}`
`c) \sqrt{8\sqrt{3}} - 2\sqrt{25\sqrt{12}} + 4\sqrt{\sqrt{192}}`
`= 2\sqrt{2}\root[4]{3} - 10\sqrt{2}\root[4]{3} + 8\root[4]{12}`
`= -8\sqrt{2}\root[4]{3} + 8\root[4]{12}`
`= -8\root[4]{12} + 8\root[4]{12}`
`= 0`
`d) \sqrt{2-\sqrt{3}}(\sqrt{6}+\sqrt{2})`
`= (\sqrt{6} + \sqrt{2})\sqrt{2-\sqrt{3}}`
`= \sqrt{6}\sqrt{2-\sqrt{3}} + \sqrt{2}\sqrt{2-\sqrt{3}}`
`= 3 - \sqrt{3} + \sqrt{3} - 1`
`= 3-1`
`= 2`
`e) \sqrt{3-\sqrt{5}} + \sqrt{3+\sqrt{5}}`
Đặt `A = \sqrt{3-\sqrt{5}} + \sqrt{3+\sqrt{5}}`
`⇒ A^2 = 3-\sqrt{5}+3+\sqrt{5}+2\sqrt{3-\sqrt{5}}\sqrt{3+\sqrt{5}}`
`⇒ A^2 = 2\sqrt{3-\sqrt{5}}\sqrt{3+\sqrt{5}} + 3 - \sqrt{5} +3+\sqrt{5}`
`⇒ A^2 = 4 + 3 + 3`
`⇒ A^2 = 10`
`⇒ A = \sqrt{10}`
`d) (\sqrt{2}+1)^3 - (\sqrt{2}-1)^3`
`= 5\sqrt{2}+7-(\sqrt{2}-1)^3`
`= 5\sqrt{2}+7 - 5\sqrt{2}+7`
`= 7 + 7`
`= 14`
