[tex]a) \ \sqrt{12} = \sqrt{4\cdot3} = \sqrt{2^{2}\cdot3} = \sqrt{2^{2}}\cdot\sqrt{3} = 2\sqrt{3}\\\\b) \ \sqrt{28} = \sqrt{4\cdot7} = \sqrt{2^{2}\cdot7} = \sqrt{2^{2}}\cdot\sqrt{7} = 2\sqrt{7}\\\\c) \ \sqrt{80} = \sqrt{16\cdot5} = \sqrt{4^{2}\cdot5} = \sqrt{4^{2}}\cdot\sqrt{5} = 4\sqrt{5}\\\\d) \ \sqrt{125} = \sqrt{25\cdot5} = \sqrt{5^{2}\cdot5} = \sqrt{5^{2}}\cdot\sqrt{5} = 5\sqrt{5}[/tex]
[tex]e) \ \sqrt[3]{32} = \sqrt[3]{8\cdot4} =\sqrt[3]{2^{3}\cdot4} = \sqrt[3]{2^{3}}\cdot\sqrt[3]{4} = 2\sqrt[3]{4}\\\\f) \ \sqrt[3]{54} = \sqrt[3]{27\cdot2} = \sqrt[3]{3^{3}\cdot2} = \sqrt[3]{3^{3}}\cdot\sqrt[3]{2} = 3\sqrt[3]{2}\\\\g) \ \sqrt[3]{-16} = -\sqrt[3]{16} = -\sqrt[3]{8\cdot2} = -\sqrt[3]{2^{3}\cdot2} =-\sqrt[3]{2^{3}}\cdot\sqrt[3]{2} =-2\sqrt[3]{2}[/tex]
[tex]h) \ \sqrt[3]{-128} = -\sqrt[3]{128} = -\sqrt[3]{64\cdot2} =-\sqrt[3]{4^{3}\cdot2} = -\sqrt[3]{4^{3}}\cdot\sqrt[3]{2} = -4\sqrt[3]{2}[/tex]
