[tex]a) \ \sqrt{2}\cdot\sqrt{5}\cdot\sqrt{3} = \sqrt{2\cdot5\cdot3}} = \sqrt{30}\\\\\\b) \ \sqrt[3]{5}\cdot\sqrt[3]{5}\cdot\sqrt[3]{2}=\sqrt[3]{5\cdot5\cdot2} = \sqrt[3]{50}\\\\\\c) \ \frac{\sqrt{6}\cdot\sqrt{5}}{\sqrt{2}} = \sqrt{\frac{6\cdot5}{2}} = \sqrt{3\cdot5} = \sqrt{15}\\\\\\d) \ \frac{\sqrt[3]{10}}{\sqrt[3]{3}\cdot\sqrt[3]{5}} = \sqrt[3]{\frac{10}{3\cdot5}} = \sqrt[3]{\frac{2}{3}}[/tex]
[tex]e) \ \frac{\sqrt{200}\cdot\sqrt{7}}{\sqrt{28}} = \sqrt{\frac{200\cdot7}{28}} = \sqrt{\frac{200}{4}} = \sqrt{50} =\sqrt{25\cdot2} = 5\sqrt{2}\\\\\\f) \ (\sqrt{15}\cdot\sqrt{4}):\sqrt{30} = \sqrt{15\cdot4}:\sqrt{30} = \sqrt{60}:\sqrt{30} = \sqrt{60:30} = \sqrt{2}\\\\\\g) \ \sqrt[3]{7}\cdot\sqrt[3]{16}:\sqrt[3]{28} = \sqrt[3]{7\cdot16}:\sqrt[3]{28} = \sqrt[3]{112}:\sqrt[3]{28} = \sqrt[3]{112:28} = \sqrt{4} = 2[/tex]
[tex]h) \ \frac{\sqrt[3]{9}\cdot\sqrt[3]{2}}{\sqrt[3]{3}} = \sqrt[3]{\frac{9\cdot2}{3}} = \sqrt[3]{3\cdot2} = \sqrt[3]{6}\\\\\\i) \ \frac{\sqrt{30}\cdot\sqrt{7}}{\sqrt{35}} = \sqrt{\frac{30\cdot7}{35}} = \sqrt{\frac{30}{5}} = \sqrt{6}[/tex]
