6.
[tex]a) \ 8\sqrt{6}-3\sqrt{6}+5\sqrt{6} = 10\sqrt{6}\\\\b) \ 21\sqrt{3}+7\sqrt{5}-\sqrt{3}+3\sqrt{5}-20\sqrt{3} = 10\sqrt{5}\\\\c) \ 32\sqrt[3]{13}+\sqrt[3]{-13} =32\sqrt[3]{13} -\sqrt[3]{13} = 31\sqrt[3]{13}\\\\d) \ \sqrt[3]{3}-\sqrt[3]{5}+6\sqrt[3]{3} -\sqrt[3]{-5}+2\sqrt[3]{5} =7\sqrt[3]{3} +\sqrt[3]{5} -(-\sqrt[3]{5}) = 7\sqrt[3]{3}+2\sq\sqrt[3]{5}[/tex]
7.
[tex]a) \ Ob = 2\cdot5\sqrt{3}+2(4\sqrt{5}+6\sqrt{3}) = 10\sqrt{3}+8\sqrt{5}+12\sqrt{3} =22\sqrt{3}+8\sqrt{5}\\\\b) \ Ob = 7\sqrt{7}+9\sqrt{11} + 6\sqrt{7}-\sqrt{11} =13\sqrt{7}+8\sqrt{11}[/tex]
8.
[tex]a)\\3\sqrt{5} = \sqrt{3^{2}\cdot5} = \sqrt{9\cdot5} = \sqrt{45}\\\\5\sqrt{3} = \sqrt{5^{2}\cdot3} = \sqrt{25\cdot3} = \sqrt{75}\\\\3\sqrt{5} < 5\sqrt{3}[/tex]
[tex]b)\\2\sqrt{12} = \sqrt{2^{2}\cdot12} = \sqrt{4\cdot12} = \sqrt{48}\\\\6\sqrt{2} = \sqrt{6^{2}\cdot2} = \sqrt{36\cdot2} = \sqrt{72}\\\\2\sqrt{12} < 6\sqrt{2}[/tex]
