`a) 4\sqrt{12} + 3\sqrt{27} - 4\sqrt{48}`

`= 4 * \sqrt{4 * 3} + 3 * \sqrt{9 * 3} - 4 * \sqrt{16 * 3}`

`= 4 * 2\sqrt{3} + 3 * 3\sqrt{3} - 4 * 4\sqrt{3}`

`= 8\sqrt{3} + 9\sqrt{3} - 16\sqrt{3}`

`= (8 + 9 - 16)\sqrt{3}`

`= 1\sqrt{3}`

`= \sqrt{3}`

`c) 2\sqrt{2} + \sqrt{(\sqrt{8} - 3)^2}`

`= 2\sqrt{2} + |\sqrt{8} - 3|`

Vì `8 < 9 \Rightarrow \sqrt{8} < \sqrt{9} \Rightarrow \sqrt{8} < 3 \Rightarrow \sqrt{8} - 3 < 0 \Rightarrow |\sqrt{8} - 3| = -( \sqrt{8} - 3 ) = 3 - \sqrt{8}`

`= 2\sqrt{2} + 3 - \sqrt{4 * 2}`

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

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

`= 3`

$e) \sqrt{25} + 2\sqrt{6} - \sqrt{24} + 3 · \sqrt[3]{8}$

$= \sqrt{5^2} + 2\sqrt{6} - \sqrt{4 · 6} + 3  · \sqrt[3]{2^3}$

`= 5 + 2\sqrt{6} - 2\sqrt{6} + 3 * 2`

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

`= 5 + 0 + 6`

`= 11`

`g) (3\sqrt{5} + 2)\sqrt{(3\sqrt{5} - 2)^2}`

`= (3\sqrt{5} + 2)|3\sqrt{5} - 2|`

Vì `3\sqrt{5} = \sqrt{45} > \sqrt{4} = 2 \Rightarrow 3\sqrt{5} - 2 > 0 \Rightarrow |3\sqrt{5} - 2| = 3\sqrt{5} - 2`

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

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

`= 9 * 5 - 4`

`= 45 - 4`

`= 41`

`i) 20\sqrt{1/5} - 3\sqrt{20} + 3\sqrt{125}`

`= 20 * \sqrt{5/25} - 3 * \sqrt{4 * 5} + 3 * \sqrt{25 * 5}`

`= 20 * (\sqrt{5}/5) - 3 * 2\sqrt{5} + 3 * 5\sqrt{5}`

`= 4\sqrt{5} - 6\sqrt{5} + 15\sqrt{5}`

`= (4 - 6 + 15)\sqrt{5}`

`= 13\sqrt{5}`

`k) 2\sqrt{28} + 3\sqrt{63} - 2\sqrt{112} - \sqrt{175}`

`= 2 * \sqrt{4 * 7} + 3 * \sqrt{9 * 7} - 2 * \sqrt{16 * 7} - \sqrt{25 * 7}`

`= 2 * 2\sqrt{7} + 3 * 3\sqrt{7} - 2 * 4\sqrt{7} - 5\sqrt{7}`

`= 4\sqrt{7} + 9\sqrt{7} - 8\sqrt{7} - 5\sqrt{7}`

`= (4 + 9 - 8 - 5)\sqrt{7}`

`= 0 * \sqrt{7}`

`= 0`

`m) (3 - (5 + \sqrt{15})/(\sqrt{5} + \sqrt{3}))(3 + (5 - \sqrt{5})/(\sqrt{5} - 1))`

`= (3 - ((\sqrt{5} * \sqrt{5} + \sqrt{5} * \sqrt{3}))/(\sqrt{5} + \sqrt{3}))(3 + ((\sqrt{5} * \sqrt{5} - \sqrt{5} * 1))/(\sqrt{5} - 1))`

`= (3 - (\sqrt{5}(\sqrt{5} + \sqrt{3}))/(\sqrt{5} + \sqrt{3}))(3 + (\sqrt{5}(\sqrt{5} - 1))/(\sqrt{5} - 1))`

`= (3 - \sqrt{5})(3 + \sqrt{5})`

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

`= 9 - 5`

`= 4`

`o) (\sqrt{28} - \sqrt{12} - \sqrt{7})\sqrt{7} + 2\sqrt{21}`

`= (\sqrt{4 * 7} - \sqrt{4 * 3} - \sqrt{7})\sqrt{7} + 2\sqrt{21}`

`= (2\sqrt{7} - 2\sqrt{3} - \sqrt{7})\sqrt{7} + 2\sqrt{21}`

`= ((2\sqrt{7} - \sqrt{7}) - 2\sqrt{3})\sqrt{7} + 2\sqrt{21}`

`= (\sqrt{7} - 2\sqrt{3})\sqrt{7} + 2\sqrt{21}`

`= \sqrt{7} * \sqrt{7} - 2\sqrt{3} * \sqrt{7} + 2\sqrt{21}`

`= 7 - 2\sqrt{21} + 2\sqrt{21}`

`= 7`

`q) 6\sqrt{27} - 2\sqrt{75} - 1/2\sqrt{300}`

`= 6 * \sqrt{9 * 3} - 2 * \sqrt{25 * 3} - 1/2 * \sqrt{100 * 3}`

`= 6 * 3\sqrt{3} - 2 * 5\sqrt{3} - 1/2* 10\sqrt{3}`

`= 18\sqrt{3} - 10\sqrt{3} - 5\sqrt{3}`

`= (18 - 10 - 5)\sqrt{3}`

`= 3\sqrt{3}`

`s) 2\sqrt{28} + 2\sqrt{63} - 3\sqrt{175} + \sqrt{112}`

`= 2 * \sqrt{4 * 7} + 2 * \sqrt{9 * 7} - 3 * \sqrt{25 * 7} + \sqrt{16 * 7}`

`= 2 * 2\sqrt{7} + 2 * 3\sqrt{7} - 3 * 5\sqrt{7} + 4\sqrt{7}`

`= 4\sqrt{7} + 6\sqrt{7} - 15\sqrt{7} + 4\sqrt{7}`

`= (4 + 6 - 15 + 4)\sqrt{7}`

`= -1\sqrt{7}`

`= -\sqrt{7}`

`u) 4\sqrt{2} - 3\sqrt{20} - 5\sqrt{8} + 2\sqrt{45}`

`= 4\sqrt{2} - 3 * \sqrt{4 * 5} - 5 * \sqrt{4 * 2} + 2 * \sqrt{9 * 5}`

`= 4\sqrt{2} - 3 * 2\sqrt{5} - 5 * 2\sqrt{2} + 2 * 3\sqrt{5}`

`= 4\sqrt{2} - 6\sqrt{5} - 10\sqrt{2} + 6\sqrt{5}`

`= (4\sqrt{2} - 10\sqrt{2}) + (-6\sqrt{5} + 6\sqrt{5})`

`= -6\sqrt{2} + 0`

`= -6\sqrt{2}`