6.
[tex]a) \ 7\sqrt{5}+2\sqrt{5} = 9\sqrt{5}\\\\b) \ \sqrt{30}\cdot\sqrt{1\frac{1}{5}} = \sqrt{30\cdot\frac{6}{5}} = \sqrt{6\cdot6} = 6\\\\c) \ \sqrt{300}-2\sqrt{3} = \sqrt{100\cdot3}-2\sqrt{3} = 10\sqrt{3}-2\sqrt{3} = 8\sqrt{3}\\\\d) \ 2\sqrt{6}\cdot\frac{1}{3}\sqrt{3} = 2\cdot\frac{1}{3}\cdot\sqrt{6\cdot3} = \frac{2}{3}\sqrt{18} = \frac{2}{3}\sqrt{9\cdot2} = \frac{2}{3}\cdot3\sqrt{2} = 2\sqrt{2}[/tex]
[tex]e) \ (\frac{5\sqrt{6}}{3})^{2} =\frac{5^{2}\cdot\sqrt{6^{2}}}{3^{2}} = \frac{25\cdot6}{9} = \frac{25\cdot2}{3}=\frac{50}{3} = 16\frac{2}{3}[/tex]
7.
[tex]a) \ 3\sqrt{17}+5 > 17\\\\b) \ \frac{\sqrt{21}}{2}-1,5 < 1\\\\c) \ 7\sqrt[3]{6}+2 > 16\\\\d) \ \frac{\sqrt[3]{25}}{3}-1 > 0[/tex]
