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`bb{a})` `\sqrt{(1-\sqrt{5})^2}+\sqrt{(\sqrt{5}-3)^2}`

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

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

`=2`

`bb{b})` `\sqrt{(3-\sqrt{2})^2}+\sqrt{(\sqrt{2}-1)^2}`

`=|3-\sqrt{2}|+|\sqrt{2}-1|`

`=3-\sqrt{2}+\sqrt{2}-1`

`=2`

`bb{c})` `\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}`

`=\sqrt{3-2. \sqrt{2} . \sqrt{3}+2}+\sqrt{3+2.\sqrt{2} . \sqrt{3}+2}`

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

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

`=|\sqrt{3}-\sqrt{2}|+|\sqrt{3}+\sqrt{2}|`

`=\sqrt{3}-\sqrt{2}+\sqrt{3}+\sqrt{2}`

`=2\sqrt{3}`

`bb{d})` `\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}`

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

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

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

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

`=2\sqrt{2}`