`a)` `A=\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}`
`=\sqrt{5+2\sqrt{5.1}+1}+\sqrt{5-2\sqrt{5.1}+1}`
`=\sqrt{(\sqrt{5}+1)^2}+\sqrt{(\sqrt{5}-1)^2}`
`=|\sqrt{5}+1|+|\sqrt{5}-1|`
`=\sqrt{5}+1+\sqrt{5}-1` (do `\sqrt{5}+1>0;\sqrt{5}-1>0)`
`=2\sqrt{5}`
`b)` `B=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}`
`=\sqrt{7-2\sqrt{7.1}+1}-\sqrt{7+2\sqrt{7.1}+1}`
`=\sqrt{(\sqrt{7}-1)^2}-\sqrt{(\sqrt{7}+1)^2}`
`=|\sqrt{7}-1|-|\sqrt{7}+1|`
`=\sqrt{7}-1-(\sqrt{7}+1)` (do `\sqrt{7}-1>0;\sqrt{7}+1>0)`
`=\sqrt{7}-1-\sqrt{7}-1`
`=-2`
`c)` `C=\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}`
`=\sqrt{11+2.3\sqrt{2}}-\sqrt{11-2.3\sqrt{2}}`
`=\sqrt{11+2\sqrt{2.9}}-\sqrt{11-2.\sqrt{2.9}}`
`=\sqrt{9+2\sqrt{2.9}+2}-\sqrt{9-2\sqrt{2.9}+2}`
`=\sqrt{(3+\sqrt{2})^2}-\sqrt{(3-\sqrt{2})^2}`
`=|3+\sqrt{2}|-|3-\sqrt{2}|`
`=3+\sqrt{2}-(3-\sqrt{2})` (do `3+\sqrt{2}>0;3-\sqrt{2}>0)`
`=3+\sqrt{2}-3+\sqrt{2}`
`=2\sqrt{2}`
`d)` `D=\sqrt{3+2\sqrt{2}}+\sqrt{6-4\sqrt{2}}`
`=\sqrt{2+2\sqrt{2.1}+1}+\sqrt{6-2.2\sqrt{2}}`
`=\sqrt{(\sqrt{2}+1)^2}+\sqrt{6-2\sqrt{4.2}}`
`=\sqrt{(1+\sqrt{2})^2}+\sqrt{4-2\sqrt{4.2}+2}`
`=\sqrt{(1+\sqrt{2})^2}+\sqrt{(2-\sqrt{2})^2}`
`=|1+\sqrt{2}|+|2-\sqrt{2}|`
`=1+\sqrt{2}+2-\sqrt{2}` (do `1+\sqrt{2}>0;2-\sqrt{2}>0)`
`=3`
`e)` `E=\sqrt{37^2-35^2}`
`=\sqrt{(37+35)(37-35)}`
`=\sqrt{72.2}`
`=\sqrt{144}`
`=12`
`f)` `F=\sqrt{65^2-63^2}`
`=\sqrt{(65+63)(65-63)}`
`=\sqrt{128.2}`
`=\sqrt{256}`
`=16`
