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$\\$ `a,sqrt{(3-2sqrt2)^2}+sqrt{(3+2sqrt2)^2}`

$\\$ `=|3-2sqrt2|+|3+2sqrt2|`

$\\$ `=3-2sqrt2+3+2sqrt2`(Vì `3>2sqrt2`)

$\\$ `=6`

$\\$ `b,sqrt{(5-2sqrt6)^2}-sqrt{(5+2sqrt6)^2}`

$\\$ `=|5-2sqrt6|-|5+2sqrt6|`

$\\$ `=5-2sqrt6-(5+2sqrt6)` (Vì `5>2sqrt6`)

$\\$ `=5-2sqrt6-5-2sqrt6`

$\\$ `=-4sqrt6`

$\\$ `c,sqrt{(2-sqrt3)^2}+sqrt{(1-sqrt3)^2}`

$\\$ `=|2-sqrt3|+|1-sqrt3|`

$\\$ `=2-sqrt3+sqrt3-1`(Vì `2>sqrt3>1`)

$\\$ `=1`

$\\$ `d,sqrt{(3+sqrt2)^2}-sqrt{(1-sqrt2)^2}`

$\\$ `=|3+sqrt2|-|1-sqrt2|`

$\\$ `=3+sqrt2-(sqrt2-1)` (Vì `sqrt2>1`)

$\\$ `=3+sqrt2-sqrt2+1`

$\\$ `=4`

$\\$ `e,sqrt{(sqrt5-sqrt2)^2}+sqrt{(sqrt5+sqrt2)^2}`

$\\$ `=|sqrt5-sqrt2|+|sqrt5+sqrt2|`

$\\$ `=sqrt5-sqrt2+sqrt5+sqrt2`(Vì `sqrt5>sqrt2`)

$\\$ `=2sqrt5`

$\\$ `f,sqrt{(sqrt2+1)^2}+sqrt{(sqrt2-5)^2}`

$\\$ `=|sqrt2+1|-|sqrt2-5|`

$\\$ `=sqrt2+1-(5-sqrt2)` (Vì `5>sqrt2`)

$\\$ `=sqrt2+1-5+sqrt2`

$\\$ `=2sqrt2-4`

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

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

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

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

`= 6`

`b)` `\sqrt{(5 - 2\sqrt{6})^2} - \sqrt{(5 + 2\sqrt{6})^2}`

`= |5 - 2\sqrt{6}| - |5 + 2\sqrt{6}|`

`= (5 - 2\sqrt{6}) - (5 + 2\sqrt{6})`

`= 5 - 2\sqrt{6} - 5 - 2\sqrt{6}`

`= -4\sqrt{6}`

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

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

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

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

`= 1`

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

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

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

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

`= 4`

`e)` `\sqrt{(\sqrt{5} - \sqrt{2})^2} + \sqrt{(\sqrt{5} + \sqrt{2})^2}`

`= |\sqrt{5} - \sqrt{2}| + |\sqrt{5} + \sqrt{2}|`

`= (\sqrt{5} - \sqrt{2}) + (\sqrt{5} + \sqrt{2})`

`= \sqrt{5} - \sqrt{2} + \sqrt{5} + \sqrt{2}`

`= 2\sqrt{5}`

`f)` `\sqrt{(\sqrt{2} + 1)^2} - \sqrt{(\sqrt{2} - 5)^2}`

`= |\sqrt{2} + 1| - |\sqrt{2} - 5|`

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

`= \sqrt{2} + 1 - 5 + \sqrt{2}`

`= 2\sqrt{2} - 4`