Đáp án+Giải thích các bước giải:
Bài 2 :
`a) (3 - \sqrt{2}) . \sqrt{11 + 6\sqrt{2}}`
`= (3 - \sqrt{2}) . \sqrt{(3 + \sqrt{2})²}`
`= (3 - \sqrt{2}) . (3 + \sqrt{2})`
`= 9 - 2`
`= 7`
`b) \sqrt{2} . \sqrt{7 + 3\sqrt{5}} - \frac{4}{\sqrt{5} - 1}`
`= \sqrt{14 + 6\sqrt{5}} - \frac{4(\sqrt{5} + 1)}{(\sqrt{5} - 1)(\sqrt{5} + 1)}`
`= \sqrt{(3 + \sqrt{5})²} - \frac{4(\sqrt{5} + 1)}{4}`
`= 3 + \sqrt{5} - \sqrt{5} - 1`
`= 2`
`c) \sqrt{27} - 6\sqrt{\frac{1}{3}} + \frac{\sqrt{3} - 3}{\sqrt{3}}`
`= 3\sqrt{3} - 2\sqrt{3} + \frac{\sqrt{3}(1 - \sqrt{3})}{\sqrt{3}}`
`= \sqrt{3} + 1 - \sqrt{3}`
`= 1`
`d) \frac{9 - 2\sqrt{3}}{3\sqrt{6} - 2\sqrt{2}}`
`= \frac{\sqrt{3}(3\sqrt{3} - 2)}{\sqrt{2}(3\sqrt{3} - 2)}`
`= \frac{\sqrt{3}}{\sqrt{2}}`
`= \frac{\sqrt{6}}{2}`
