`1)` `\sqrt{18-4\sqrt{8}}`
`=\sqrt{16-4.2\sqrt{2}+2}`
`=\sqrt{4^2-2.4.\sqrt{2}+2}`
`=\sqrt{(4-\sqrt{2})^2}`
`=|4-\sqrt{2}|=4-\sqrt{2}` (vì `4>\sqrt{2})`
$\\$
`2)` Sửa đề
`\qquad \sqrt{16+6\sqrt{7}}`
`=\sqrt{3^2+2.3.\sqrt{7}+7}`
`=\sqrt{(3+\sqrt{7})^2}`
`=|3+\sqrt{7}|=3+\sqrt{7}`
$\\$
`3)` `\sqrt{46+6\sqrt{5}}`
`=\sqrt{45+6\sqrt{5}+1}`
`=\sqrt{(3\sqrt{5})^2+2.3\sqrt{5}.1+1^2}`
`=\sqrt{(3\sqrt{5}+1)^2}`
`=|3\sqrt{5}+1|=3\sqrt{5}+1`
$\\$
`4)` `\sqrt{25+4\sqrt{6}}`
`=\sqrt{24+4\sqrt{6}+1}`
`=\sqrt{(2\sqrt{6})^2+2.2\sqrt{6}.1+1^2}`
`=\sqrt{(2\sqrt{6}+1)^2}`
`=|2\sqrt{6}+1|=2\sqrt{6}+1`
$\\$
`5)` `\sqrt{21-6\sqrt{6}}`
`=\sqrt{18-6\sqrt{6}+3}`
`=\sqrt{(3\sqrt{2})^2-2.3\sqrt{2}.\sqrt{3}+3}`
`=\sqrt{(3\sqrt{2}-\sqrt{3})^2}`
`=|3\sqrt{2}-\sqrt{3}|=3\sqrt{2}-\sqrt{3}`
(Vì `3\sqrt{2}>\sqrt{3}=>3\sqrt{2}-\sqrt{3}>0`)
