`1)` `\sqrt{(1-\sqrt{2012})^2}.\sqrt{2013+2\sqrt{2012}}`
`=|1-\sqrt{2012}|.\sqrt{2012+2\sqrt{2012.1}+1}`
`=(\sqrt{2012}-1).\sqrt{(\sqrt{2012}+1)^2}` (do `1-\sqrt{2012}<0)`
`=(\sqrt{2012}-1).|\sqrt{2012}+1|`
`=(\sqrt{2012}-1)(\sqrt{2012}+1)` (do `\sqrt{2012}+1>0)`
`=2012-1`
`=2011`
`2)` `\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}`
`=\sqrt{7+2.2\sqrt{3}}-\sqrt{7-2.2\sqrt{3}}`
`=\sqrt{7+2\sqrt{4.3}}-\sqrt{7-2\sqrt{4.3}}`
`=\sqrt{4+2\sqrt{4.3}}-\sqrt{4-2\sqrt{4.3}+3}`
`=\sqrt{(\sqrt{4}+\sqrt{3})^2}-\sqrt{(\sqrt{4}-\sqrt{3})^2}`
`=|2+\sqrt{3}|-|2-\sqrt{3}|`
`=2+\sqrt{3}-(2-\sqrt{3})` (do `2+\sqrt{3}>0;2-\sqrt{3}>0)`
`=2+\sqrt{3}-2+\sqrt{3}`
`=2\sqrt{3}`