Đáp án+Giải thích các bước giải:
`a) \sqrt{\frac{1}{3}} + \frac{2}{3\sqrt{2}} - \frac{2}{\sqrt{3}} . \sqrt{\frac{5}{12} + \frac{1}{\sqrt{6}}}`
`= \frac{1}{\sqrt{3}} + \frac{2\sqrt{2}}{6} - \frac{2}{\sqrt{3}} . \sqrt{\frac{5 + 2\sqrt{6}}{12}}`
`= \frac{2\sqrt{3}}{6} + \frac{2\sqrt{2}}{6} - \frac{2}{\sqrt{3}} . \sqrt{\frac{(\sqrt{2} + \sqrt{3})²}{12}}`
`= \frac{2\sqrt{3} + 2\sqrt{2}}{6} - \frac{2}{\sqrt{3}} . \frac{\sqrt{2} + \sqrt{3}}{2\sqrt{3}}`
`= \frac{2\sqrt{3} + 2\sqrt{2} - 2\sqrt{2} - 2\sqrt{3}}{6}`
`= 0`
`b) \frac{4}{2 - \sqrt{6}} + 3 . \sqrt{a} + \frac{2\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}`
`= frac{4}{\sqrt{2}(\sqrt{2} - \sqrt{3})} + 3 . \frac{\sqrt{2}}{\sqrt{3}} - \frac{2\sqrt{3} - \sqrt{2}}{\sqrt{2} - \sqrt{3}}`
`= \frac{2\sqrt{2} - 2\sqrt{3} + \sqrt{2}}{\sqrt{2} - \sqrt{3}} + \sqrt{6}`
`= \frac{-2\sqrt{3} + 3\sqrt{2}}{\sqrt{2} - \sqrt{3}} + \sqrt{6}`
`= \frac{-\sqrt{6}(\sqrt{2} - \sqrt{3})}{\sqrt{2} - \sqrt{3}} + \sqrt{6}`
`= -\sqrt{6} + \sqrt{6}`
`= 0`
