19.
[tex]a) \ \sqrt{\frac{81}{16}} = \frac{\sqrt{81}}{\sqrt{16}} = \frac{9}{4} = 2\frac{1}{4}\\\\b) \ \sqrt{\frac{196}{25}} = \frac{14}{5} = 2\frac{4}{5}\\\\c) \ \sqrt{3\frac{1}{16}} = \sqrt{\frac{49}{16}} = \frac{7}{4} = 1\frac{3}{4}\\\\d) \ \sqrt{1\frac{9}{16}} = \sqrt{\frac{25}{16}} =\frac{5}{4} = 1\frac{1}{4}\\\\e) \ \sqrt{0,04} = 0,2\\\\f) \ \sqrt{2,25} = \sqrt{1,5^{2}} = 1,5[/tex]
[tex]g) \ \sqrt{23,04} = \sqrt{4,8^{2}} = 4,8\\\\h) \ \sqrt{12,10} = \sqrt{4\cdot3,025} = 2\sqrt{3,025}\\\\i) \ \sqrt{\frac{32}{81}} = \frac{\sqrt{32}}{\sqrt{81}} = \frac{\sqrt{16\cdot2}}{9} = \frac{4\sqrt{2}}{9}\\\\j) \ \sqrt{\frac{48}{147}}=\frac{\sqrt{48}}{\sqrt{147}} = \frac{\sqrt{16\cdot3}}{\sqrt{147}}=\frac{4\sqrt{3}}{\sqrt{147}}\cdot\frac{\sqrt{147}}{\sqrt{147}}=\frac{4\sqrt{3\cdot147}}{147}= \frac{4\sqrt{441}}{147}=\frac{4\cdot21}{147} = \frac{84}{147}[/tex]
24.
[tex]a) \ \sqrt[3]{-343} =\sqrt[3]{(-7)^{3}} = -7\\\\b) \ \sqrt[3]{27} = \sqrt[3]{3^{3}} = 3\\\\c) \ \sqrt[3]{-216} = \sqrt[3]{(-6)^{3}} = -6\\\\d) \ \sqrt[3]{0} = 0\\\\e) \ \sqrt[3]{-1 \ 000 \ 000} = \sqrt[3]{(-100)^{3}} = -100\\\\f) \ \sqrt[3]{512} = \sqrt[3]{8^{3}} = 8[/tex]
25.
[tex]a) \ \sqrt[3]{192} =\sqrt[3]{64\cdot3} = \sqrt[3]{4^{3}\cdot3} = 4\sqrt[3]{3}\\\\b) \ \sqrt[3]{1250} = \sqrt[3]{125\cdot10} = 5\sqrt[3]{10}\\\\c) \ \sqrt[3]{-135} = \sqrt[3]{-27\cdot5} = -3\sqrt[3]{5}\\\\d) \ \sqrt[3]{432} = \sqrt[3]{216\cdot2} = \sqrt[3]{6^{3}\cdot2} = 6\sqrt[3]{2}\\\\e) \ \sqrt[3]{72} = \sqrt[3]{8\cdot9} = 2\sqrt[3]{9}\\\\f) \ \sqrt[3]{1728} =\sqrt[3]{12^{3}} = 12[/tex]
