1.
[tex]a) \ \sqrt{49} = \sqrt{7^{2}} = 7\\\\b) \ \sqrt{100} = \sqrt{10^{2}} = 10\\\\c) \ \sqrt{36} = \sqrt{6^{2}} = 6\\\\d) \ \sqrt{25} = \sqrt{5^{2}} = 5[/tex]
[tex]e) \ \sqrt{64} = \sqrt{8^{2}} = 8\\\\f) \ \sqrt{16} = \sqrt{4^{2}} = 4\\\\g) \ \sqrt{81} = \sqrt{9^{2}} = 9\\\\h) \ \sqrt[3]{8} = \sqrt[3]{2^{3}} = 2\\\\i) \ \sqrt[3]{27} = \sqrt[3]{3^{3}} = 3[/tex]
[tex]j) \ \sqrt{\frac{9}{49}} = \frac{\sqrt{9}}{\sqrt{49}} = \frac{\sqrt{3^{2}}}{\sqrt{7^{2}}} = \frac{3}{7}\\\\k) \ \sqrt{1\frac{1}{4}} = \sqrt{\frac{1\cdot4+1}{4}} = \sqrt{\frac{5}{4}}=\frac{\sqrt{5}}{\sqrt{4}} = \frac{\sqrt{5}}{2}\\\\l) \ \sqrt{400} = \sqrt{20^{2}} = 20\\\\l.)\sqrt[3]{125} = \sqrt[3]{5^{3}} = 5[/tex]
2.
[tex]a) \ (\sqrt{7})^{2} = 7\\\\b) \ (\sqrt[3]{9})^{3} =9\\\\c) \ \sqrt{2}\cdot\sqrt{18} = \sqrt{2\cdot18} = \sqrt{36} = \sqrt{6^{2}} = 6[/tex]
[tex]d) \ \sqrt{36\cdot9} = \sqrt{36}\cdot\sqrt{9} = \sqrt{6^{2}}\cdot\sqrt{3^{2}} = 6\cdot3 = 18\\\\e) \ \sqrt{250}:\sqrt{10} = \sqrt{250:10} = \sqrt{25} = \sqrt{5^{2}} = 5\\\\f) \ \sqrt{49\cdot25} = \sqrt{49}\cdot\sqrt{25} = \sqrt{7^{2}}\cdot\sqrt{5^{2}} = 7\cdot5 = 35[/tex]
3.
[tex]a) \ 5\sqrt{7}+3\sqrt{7} = \sqrt{7}\cdot(5+3) = 8\sqrt{7}\\\\b) \ 12\sqrt{5}-8\sqrt{5} = 4\sqrt{5}\\\\c) \ 6\sqrt{2}\cdot5\sqrt{3} = 6\cdot5\cdot\sqrt{2\cdot3} = 30\sqrt{6}\\\\d) \ \frac{8\sqrt{2}}{4\sqrt{2}} = \frac{8}{4}\cdot\sqrt{\frac{2}{2}} = 2\cdot\sqrt{1} = 2\cdot1 = 2[/tex]
