$\sqrt{5+\sqrt{21}} - \sqrt{5-\sqrt{21}}$

Đáp án:

`A = \sqrt{5+\sqrt{21}} - \sqrt{5-\sqrt{21}}` 
`\sqrt{2} . A = \sqrt{2} .( \sqrt{5+\sqrt{21}} - \sqrt{5-\sqrt{21}})`
`\sqrt{2} . A =\sqrt{10+2\sqrt{21}} - \sqrt{10-2\sqrt{21}}`
`\sqrt{2} . A=\sqrt{7 + 2.\sqrt{7}.\sqrt{3} +3 } - \sqrt{7 - 2.\sqrt{7}.\sqrt{3} +3 }`
`\sqrt{2} . A= \sqrt{(\sqrt{7} +\sqrt{3})^2 } - \sqrt{(\sqrt{7}-\sqrt{3})^2 }`
`\sqrt{2} . A = \sqrt{7} + \sqrt{3} - | \sqrt{7} - \sqrt{3}|`
`\sqrt{2} . A =\sqrt{7} + \sqrt{3} - (\sqrt{7} - \sqrt{3})`
`\sqrt{2} . A = \sqrt{7} + \sqrt{3} - \sqrt{7} + \sqrt{3}`

`\sqrt{2} . A = 2 \sqrt{3}`

`A = \frac{2 \sqrt{3}}{\sqrt{2}} = \sqrt{6}`