C.
[tex]a) \ 2\sqrt{3}+3\sqrt{3}-\sqrt{3} = 5\sqrt{3}-\sqrt{3} = 4\sqrt{3}\\\\b) \ 3\sqrt{5}-4\sqrt{5}+\sqrt{5} = 4\sqrt{5}-4\sqrt{5} = 0\\\\c) \ 4\sqrt{2}+5\sqrt{2} = 9\sqrt{2}\\\\d) \ 5\sqrt{7}-3\sqrt{7} = 2\sqrt{7}\\\\e) \ \sqrt{11}-5\sqrt{11}+7\sqrt{11} = 8\sqrt{11}-5\sqrt{11} = 3\sqrt{11}\\\\f) \ 6\sqrt{6}+2\sqrt{6}-7\sqrt{6} = 8\sqrt{6}-7\sqrt{6} = \sqrt{6}[/tex]
D.
[tex]a) \ 4\sqrt{3}-\sqrt{27}-2\sqrt{12} = 4\sqrt{3}-\sqrt{9\cdot3} -2\sqrt{4\cdot3} = 4\sqrt{3}-3\sqrt{3}-2\cdot2\sqrt{3} =\\\\=4\sqrt{3}-3\sqrt{3}-4\sqrt{3} = -3\sqrt{3}[/tex]
[tex]b) \ 2\sqrt{125} -3\sqrt{45}+4\sqrt{5} =2\sqrt{25\cdot5}-3\sqrt{9\cdot5} + 4\sqrt{5} = 2\cdot5\cdot\sqrt{5}-3\cdot3\cdot\sqrt{5}+4\sqrt{5}=\\\\=10\sqrt{5}-9\sqrt{5}+4\sqrt{5} = 14\sqrt{5}-9\sqrt{5} = 5\sqrt{5}[/tex]
[tex]c) \ \sqrt{200}-\sqrt{162} + \sqrt{2} =\sqrt{100\cdot2} - \sqrt{81\cdot2}+\sqrt{2} = 10\sqrt{2}-9\sqrt{2}+\sqrt{2} =\\\\=11\sqrt{2}-9\sqrt{2} = 2\sqrt{2}[/tex]
[tex]d) \ \sqrt{63}+3\sqrt{7}-\sqrt{28} =\sqrt{9\cdot7} + 3\sqrt{7}-\sqrt{4\cdot7} = 3\sqrt{7}+3\sqrt{7}-2\sqrt{7} =\\\\= 6\sqrt{7}-2\sqrt{7} =4\sqrt{7}[/tex]
[tex]e) \ 5\sqrt{11}-\sqrt{44}+\sqrt{99} = 5\sqrt{11}-\sqrt{4\cdot11}+\sqrt{9\cdot11} = 5\sqrt{11}-2\sqrt{11}+3\sqrt{11} =\\\\=8\sqrt{11}-2\sqrt{11} =6\sqrt{11}[/tex]
[tex]f) \ \sqrt{20}-\sqrt{45}+\sqrt{500} =\sqrt{4\cdot5}-\sqrt{9\cdot5} + \sqrt{100\cdot5} = 2\sqrt{5}-3\sqrt{5}+10\sqrt{5}=\\\\=12\sqrt{5}-3\sqrt{5} = 9\sqrt{5}[/tex]
