`a)` `\sqrt{7+2\sqrt{10}}`
`=\sqrt{5+2\sqrt{5.2}+2}`
`=\sqrt{(\sqrt{5}+\sqrt{2})^2}`
`=|\sqrt{5}+\sqrt{2}|`
`=\sqrt{5}+\sqrt{2}` (do `\sqrt{5}+\sqrt{2}>0)`
`b)` `\sqrt{17-12\sqrt{2}}`
`=\sqrt{17-2.6\sqrt{2}}`
`=\sqrt{17-2\sqrt{72}}`
`=\sqrt{8-2\sqrt{8.9}+9}`
`=\sqrt{(\sqrt{8}-\sqrt{9})^2}`
`=|\sqrt{8}-\sqrt{9}|`
`=\sqrt{9}-\sqrt{8}` (do `\sqrt{8}-\sqrt{9}<0)`
`=3-2\sqrt{2}`
`c)` `\sqrt{9+4\sqrt{5}}`
`=\sqrt{9+2.2\sqrt{5}}`
`=\sqrt{5+2\sqrt{5.4}+4}`
`=\sqrt{(\sqrt{5}+\sqrt{4})^2}`
`=|\sqrt{5}+2|`
`=\sqrt{5}+2` (do `\sqrt{5}+2>0)`
`d)` `\sqrt{11-6\sqrt{2}}`
`=\sqrt{11-2.3\sqrt{2}}`
`=\sqrt{9-2\sqrt{9.2}+2}`
`=\sqrt{(\sqrt{9}-\sqrt{2})^2}`
`=|3-\sqrt{2}|`
`=3-\sqrt{2}` (do `3-\sqrt{2}>0)`
