2.
[tex]a) \ 1089 = 3^{2}\cdot11^{2}\\\\\sqrt{1089} = \sqrt{3^{2}\cdot11^{2}} = 3\cdot11 = 33\\\\\\b) \ 676 = 2^{2}\cdot13^{2}\\\\\sqrt{676} = \sqrt{2^{2}\cdot13^{2}} = 2\cdot13 = 26\\\\\\c) \ 1764=2^{2}\cdot3^{2}\cdot7^{2}\\\\\sqrt{1764} = \sqrt{2^{2}\cdot3^{2}\cdot7^{2}} = 2\cdot3\cdot7 = 42[/tex]
[tex]d) \ 4356 = 2^{2}\cdot3^{2}\cdot11^{2}\\\\\sqrt{4356} = \sqrt{2^{2}\cdot3^{2}\cdot11^{2}} = 2\cdot3\cdot11 = 66[/tex]
[tex]e) \ 7056=2^{4}\cdot3^{2}\cdot7^{2}\\\\\sqrt{7056} = \sqrt{2^{4}\cdot3^{2}\cdot7^{2}} = 2^{2}\cdot3\cdot7 = 4\cdot21 = 84[/tex]
[tex]f) \ 19600 = 2^{4}\cdot5^{2}\cdot7^{2}\\\\\sqrt{19600} = \sqrt{2^{4}\cdot5^{2}\cdot7^{2}} = 2^{2}\cdot5\cdot7 = 4\cdot35 = 140[/tex]
3.
[tex]a) \ \sqrt{2}\cdot\sqrt{8} = \sqrt{2\cdot8} = \sqrt{16} = 4\\\\b) \ \sqrt{3}\cdot\sqrt{12} = \sqrt{3\cdot12} = \sqrt{36} = 6\\\\c) \ \sqrt{5}\cdot\sqrt{20} = \sqrt{5\cdot20} = \sqrt{100} = 10\\\\d) \ \sqrt{2}\cdot\sqrt{23} = \sqrt{2\cdot32} = \sqrt{64} = 8[/tex]
[tex]e) \ \frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}} = \sqrt{9} = 3\\\\f) \ \frac{\sqrt{12}}{\sqrt{3}} = \sqrt{\frac{12}{3}} = \sqrt{4} = 2\\\\g) \ \sqrt{45}:\sqrt{5} = \sqrt{45:5} = \sqrt{9} = 3\\\\h) \ \sqrt{75}:\sqrt{3} = \sqrt{75:3} = \sqrt{25} = 5[/tex]
