Đáp án + Giải thích các bước giải:
`1.`
`\sqrt{4-2\sqrt{3}}`
`= \sqrt{(\sqrt{1})^2(\sqrt{3})^2-2\sqrt{3}+(\sqrt{1})^2}`
`= \sqrt{(1*\sqrt{3}-1)^2}`
`= |\sqrt{3} - 1|`
`= \sqrt{3} - 1`
`->` đpcm
`2.`
`\sqrt{9-4\sqrt{5}} - \sqrt{5}`
`= \sqrt{(\sqrt{1})^2(\sqrt{5})^2-4\sqrt{5}+(\sqrt{4})^2} - \sqrt{5}`
`= \sqrt{(1*\sqrt{5}-2)^2} - \sqrt{5}`
`= |\sqrt{5} - 2| - \sqrt{5}`
`= \sqrt{5} - 2 - \sqrt{5}`
`= -2`
`->` đpcm
`3.`
`\sqrt{23+8\sqrt{7}} - \sqrt{7}`
`= \sqrt{(\sqrt{1})^2(\sqrt{7})^2+8\sqrt{7}(\sqrt{16})^2} - \sqrt{7}`
`= \sqrt{(1*\sqrt{7}+4)^2} - \sqrt{7}`
`= |\sqrt{7}+4| - \sqrt{7}`
`= \sqrt{7} + 4 - \sqrt{7}`
`= 4`
`->` đpcm
`4.`
`\sqrt{11+6\sqrt{2}} - 3`
`= \sqrt{(\sqrt{1})^2(\sqrt{2})^2+6\sqrt{2}+(\sqrt{9})^2} - 3`
`= \sqrt{(1*\sqrt{2}+3)^2} - 3`
`= |\sqrt{2}+3| - 3`
`= \sqrt{2} + 3 - 3`
`= \sqrt{2}`
`->` đpcm
`5.`
`\sqrt{9-4\sqrt{5}} - \sqrt{5}`
`= \sqrt{(\sqrt{1})^2(\sqrt{5})^2-4\sqrt{5}+(\sqrt{4})^2} - \sqrt{5}`
`= \sqrt{(1*\sqrt{5}-2)^2} - \sqrt{5}`
`= |\sqrt{5}-2| - \sqrt{5}`
`= \sqrt{5} - 2 - \sqrt{5}`
`= -2`
`->` đpcm
`6.`
`\sqrt{10-2\sqrt{21}} + \sqrt{3}`
`= \sqrt{(\sqrt{7})^2-2\sqrt{7}\sqrt{3}+3} + \sqrt{3} `
`= \sqrt{(\sqrt{7}-\sqrt{3})^2} + \sqrt{3}`
`= |\sqrt{7} - \sqrt{3}| + \sqrt{3}`
`= \sqrt{7} - \sqrt{3} + \sqrt{3}`
`= \sqrt{7}`
`->` đpcm
