`1, 2sqrt{9-4sqrt{2}}+3sqrt{3+2sqrt{2}}`
`=2sqrt{8-2.2sqrt{2}+1}+3sqrt{2+2sqrt{2}+1}`
`=2sqrt{(2sqrt{2}-1)^2}+3sqrt{(sqrt{2}+1)^2}`
`=2|2\sqrt{2}-1|+3|\sqrt{2}+1|`
`=2(2sqrt{2}-1)+3(sqrt{2}+1)`
`=4sqrt{2}-2+3sqrt{2}+3`
`=7sqrt{2}+1`
`2, \sqrt{11+6sqrt{2}}-3sqrt{(2sqrt{2}-3)^2}+(2+sqrt{2})/(1+sqrt{2})`
`=\sqrt{2+2.3.\sqrt{2}+9}-3|2\sqrt{2}-3|+((2+sqrt{2})(1-sqrt{2}))/(1-2)`
`=\sqrt{(\sqrt{2}+3)^2}-3(3-2\sqrt{2})-(2-2sqrt{2}+sqrt{2}-2)`
`=|\sqrt{2}+3|-9+6sqrt{2}+sqrt{2}`
`=\sqrt{2}+3-9+7sqrt{2}`
`=8sqrt{2}-6`
`3, (1/(\sqrt{5}-2)-59/(3\sqrt{7}-2))(sqrt{5}+3sqrt{7})`
`=((\sqrt{5}+2)/(5-4)-(59(3sqrt{7}+2))/(63-4))(sqrt{5}+3sqrt{7})`
`=(sqrt{5}+2-(59(3sqrt{7}+2))/59)(sqrt{5}+3sqrt{7})`
`=(sqrt{5}+2-3sqrt{7}-2)(sqrt{5}+3sqrt{7})`
`=(sqrt{5}-3sqrt{7})(sqrt{5}+3sqrt{7})`
`=5-63`
`=-58`
`4, (2sqrt{3+sqrt{5-sqrt{13+sqrt{48}}}})/(\sqrt{6}+sqrt{2})`
`=(2sqrt{3+sqrt{5-sqrt{13+4sqrt{3}}}})/(sqrt{6}+sqrt{2})`
`=(2sqrt{3+sqrt{5-sqrt{(2sqrt{3}+1)^2}}})/(sqrt{6}+sqrt{2})`
`=(2sqrt{3+sqrt{5-2sqrt{3}-1}})/(sqrt{6}+sqrt{2})`
`=(2sqrt{3+sqrt{4-2sqrt{3}}})/(sqrt{6}+sqrt{2})`
`=(2sqrt{3+sqrt{(sqrt{3}-1)^2}})/(sqrt{6}+sqrt{2})`
`=(2sqrt{3+\sqrt{3}-1})/(sqrt{6}+sqrt{2})`
`=(2sqrt{2+sqrt{3}})/(sqrt{6}+sqrt{2})`
`=(2sqrt{4+2sqrt{3}})/(2sqrt{3}+2)`
`=(2sqrt{(\sqrt{3}+1)^2})/(2(sqrt{3}+1))`
`=(2(sqrt{3}+1))/(2(sqrt{3}+1))`
`=1`
