a) `\sqrt{17-3\sqrt{32}}-\sqrt{17+3\sqrt{32}}`
`=\sqrt{9-2.2\sqrt{2}.3+8}-\sqrt{9+2.2\sqrt{2}.3+8}`
`=\sqrt{(3-\sqrt{8})^2}-\sqrt{(3+\sqrt{8})^2}`
`=|3-\sqrt{8}|-|3+\sqrt{8}|`
`=3-\sqrt{8}-3-\sqrt{8}`
`=2\sqrt{8}`
`=4\sqrt{2}`
b) `(\sqrt{3}-\sqrt{2})(\sqrt{7+4\sqrt{3})`
`=(\sqrt{3}-\sqrt{2})(\sqrt{2+2.2.\sqrt{3}+\sqrt{3}})`
`=(\sqrt{3}-\sqrt{2})(\sqrt{(2+\sqrt{3})^2)`
`=(\sqrt{3}-\sqrt{2})|2+\sqrt{3}|`
`=(\sqrt{3}-\sqrt{2})(2+\sqrt{3})`
`=(\sqrt{3})^2-(\sqrt{2})^2`
`=3-2`
`=1`
c) `(2+\sqrt{5})\sqrt{9-4\sqrt{5}}`
`=(2+\sqrt{5})\sqrt{5-2.\sqrt{5}.2+4}`
`=(2+\sqrt{5})\sqrt{(\sqrt{5}-2)^2}`
`=(2+\sqrt{5})|\sqrt{5}-2|`
`=(2+\sqrt{5})(\sqrt{5}-2)`
`=(\sqrt{5})^2-4`
`=5-4`
`=1`
8) `(3\sqrt{2}+\sqrt{10})\sqrt{28-12\sqrt{5}}`
`=(3\sqrt{2}+\sqrt{10})\sqrt{18-2.3\sqrt{2}.\sqrt{10}+10}`
`=(3\sqrt{2}+\sqrt{10})\sqrt{(3\sqrt{2}-\sqrt{10})^2}`
`=(3\sqrt{2}+\sqrt{10})|3\sqrt{2}-\sqrt{10}|`
`=(3\sqrt{2}+\sqrt{10})(3\sqrt{2}-\sqrt{10})`
`=(3\sqrt{2})^2-(\sqrt{10})^2`
`=18-10`
`=8`
