`a)` `\sqrt{(\sqrt{2}-2)^2}`
`=|\sqrt{2}-2|`
`=2-\sqrt{2}` (do `\sqrt{2}-2<0)`
`b)` `\sqrt{3+2\sqrt{2}}`
`=\sqrt{2+2\sqrt{2.1}+1}`
`=\sqrt{(\sqrt{2}+1)^2}`
`=|\sqrt{2}+1|`
`=\sqrt{2}+1` (do `\sqrt{2}+1>0)`
`c)` `\sqrt{9+4\sqrt{5}}`
`=\sqrt{9+2.2\sqrt{5}}`
`=\sqrt{4+2\sqrt{4.5}+5}`
`=\sqrt{(2+\sqrt{5})^2}`
`=|2+\sqrt{5}|`
`=2+\sqrt{5}` (do `2+\sqrt{5}>0)`
`d)` `\sqrt{(3+\sqrt{11})^2}`
`=|3+\sqrt{11}|`
`=3+\sqrt{11}` (do `3+\sqrt{11}>0)`
`e)` `\sqrt{(3+2x)^2}`
`=|3+2x|`
`f)` `\sqrt{(x-3)^2}`
`=|x-3|`
