[tex](2\sqrt{5})^{2} =2^{2}\cdot\sqrt{5}^{2} = 4\cdot5 = 20\\\\\\(\sqrt[3]{2})^{3}=2\\\\\\\frac{2\sqrt{3}\cdot3\sqrt{10}}{\sqrt{5}} = \frac{6\sqrt{3\cdot10}}{\sqrt{5}} = 6\sqrt{\frac{3\cdot10}{5}} = 6\sqrt{3\cdot2} = 6\sqrt{6}\\\\\\\frac{\sqrt{120}}{\sqrt{10}}:\sqrt{3} = \sqrt{\frac{120}{10}}:\sqrt{3} = \sqrt{12}:\sqrt{3} = \sqrt{12:3} = \sqrt{4} = \sqrt{2^{2}} = 2[/tex]
[tex]7\sqrt{8}-3\sqrt{50}+2\sqrt{18} = 7\sqrt{4\cdot2}-3\sqrt{25\cdot2}+2\sqrt{9\cdot2} =\\\\=7\sqrt{2^{2}\cdot2}-3\sqrt{5^{2}\cdot2}+2\sqrt{3^{2}\cdot2} =7\cdot2\sqrt{2}-3\cdot5\sqrt{2}+2\cdot3\sqrt{2} =\\\\= 14\sqrt{2}-15\sqrt{2}+6\sqrt{2} =5\sqrt{2}[/tex]
[tex]\sqrt{12}=5\sqrt{3} = \sqrt{4\cdot3}+5\sqrt{3}+\sqrt{2^{2}\cdot3}+5\sqrt{3} = 2\sqrt{3}+5\sqrt{3} = 7\sqrt{3}[/tex]
[tex]\frac{\sqrt{18}-\sqrt{32}}{\sqrt{12}} = \frac{\sqrt{9\cdot2}-\sqrt{16\cdot2}}{\sqrt{4\cdot3}} = \frac{3\sqrt{2}-4\sqrt{2}}{2\sqrt{3}} = \frac{-\sqrt{2}}{2\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = -\frac{\sqrt{2\cdot3}}{2\cdot3} = -\frac{\sqrt{6}}{6}[/tex]
[tex]2\sqrt{2}\cdot\sqrt{3}-\frac{1}{6}\sqrt{24} = 2\sqrt{2\cdot3}-\frac{1}{6}\sqrt{4\cdot6}=2\sqrt{6}-\frac{1}{6}\cdot2\sqrt{6} =(\frac{12}{6}-\frac{1}{6})\sqrt{6} = \\\\=2\sqrt{6}-\frac{1}{3}\sqrt{6} =(\frac{6}{3}-\frac{1}{3})\sqrt{6} = \frac{5}{3}\sqrt{6}[/tex]
[tex]\sqrt{12}\cdot\sqrt{24}\cdot\sqrt{2} = \sqrt{12\cdot24\cdot2} = \sqrt{12\cdot2\cdot24} = \sqrt{24\cdot24} = \sqrt{24^{2}} = 24[/tex]
[tex]\sqrt{128:2}:\sqrt{16+9} = \sqrt{64}:\sqrt{25} = \sqrt{\frac{64}{25}}=\frac{8}{5} = 1\frac{3}{5}[/tex]
