`a)\sqrt{3+2\sqrt{2}}`

`=\sqrt{2+2\sqrt{2}+1}`

`=\sqrt{(\sqrt{2})^2+2.\sqrt{2}.1+1^2}`

`=\sqrt{(\sqrt{2}+1)^2}`

`=|\sqrt{2}+1|`

`=\sqrt{2}+1`

`c)\sqrt{21-4\sqrt{17}}`

`=\sqrt{17-4\sqrt{17}+4}`

`=\sqrt{(\sqrt{17})^2-2.\sqrt{17}.2+2^2}`

`=\sqrt{(\sqrt{17}-2)^2}`

`=|\sqrt{17}-2|`

`=\sqrt{17}-2`

`e)\sqrt{46-6\sqrt{5}}`

`=\sqrt{45-6\sqrtt{5}+1}`

`=\sqrt{(3\sqrt{5})^2-2.3\sqrt{5}.1+1^2}`

`=\sqrt{(3\sqrt{5}-1)^2}`

`=|3\sqrt{5}-1|`

`=3\sqrt{5}-1.`