[tex]\sqrt{12}\cdot\sqrt{3} = \sqrt{12\cdot3} = \sqrt{36} = \sqrt{6^{2}} = 6\\\\\sqrt{2}\cdot\sqrt{450} =\sqrt{2\cdot450}= \sqrt{900} = \sqrt{30^{2}} = 30\\\\\sqrt[3]{32}\cdot\sqrt[3]{2} = \sqrt[3]{32\cdot2} = \sqrt[3]{64} = \sqrt[3]{4^{3}} = 4[/tex]
[tex]\sqrt[3]{4}\cdot\sqrt[3]{-2000} =\sqrt[3]{4\cdot(-2000)} = \sqrt[3]{-8000} = \sqrt[3]{(-20)^{3}} = -20[/tex]
[tex]\sqrt{200}:\sqrt{8} = \sqrt{200:8} = \sqrt{25} = \sqrt{5^{2}} = 5\\\\\frac{\sqrt{80}}{\sqrt{5}} = \sqrt{\frac{80}{5}} = \sqrt{16} = \sqrt{4^{2}} = 4\\\\\frac{\sqrt[3]{1000}}{\sqrt[3]{8}} = \sqrt[3]{\frac{1000}{8}} = \sqrt[3]{125} = \sqrt[3]{5^{3}} = 5[/tex]
[tex]4\sqrt{2}\cdot3\sqrt{8} = 4\cdot3\sqrt{2\cdot8} = 12\sqrt{16} = 12\sqrt{4^{2}} = 12\cdot4 = 48\\\\5\sqrt[3]{9}\cdot6\sqrt[3]{3}=5\cdot6\sqrt[3]{9\cdot3} = 30\sqrt[3]{3^{3}} = 30\cdot3 = 90[/tex]
