1.
[tex]\sqrt{25} = \sqrt{5^{2}} = 5\\\\\sqrt{0,09} = \sqrt{0,3^{2}} = 0,3\\\\\sqrt{1,69} = \sqrt{1,3^{2}} = 1,3\\\\\\\sqrt{2\frac{7}{9}} = \sqrt{\frac{25}{9}} = \frac{\sqrt{25}}{\sqrt{9}} = \frac{5}{3} = 1\frac{2}{3}\\\\\sqrt{\frac{64}{81}} = \frac{\sqrt{64}}{\sqrt{81}} = \frac{8}{9}\\\\\sqrt[3]{125} = \sqrt[3]{5^{3}} = 5\\\\\sqrt[3]{-27}} = \sqrt[3]{(-3)^{3}} =-3[/tex]
2.
[tex]\sqrt{1\frac{1}{4}} =\sqrt{\frac{5}{4}} \ - \ liczba \ niewymierna\\\\\sqrt[3]{-25} \ - \ liczba \ niewymierna\\\\\sqrt{27} = \sqrt{9\cdot3} = 3\sqrt{3} \ - \ liczba \ niewymierna\\\\\underline{\sqrt{1\frac{11}{25}} = \sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}}=\frac{6}{5}} \ - \ liczba \ wymierna[/tex]
3.
[tex]\sqrt{50} =\sqrt{25\cdot2} = \sqrt{25}\cdot\sqrt{2} = 5\sqrt{2}\\\\\sqrt{112} = \sqrt{16\cdot7} =\sqrt{16}\cdot\sqrt{7} = 4\sqrt{7}\\\\\sqrt[3]{88} = \sqrt[3]{8\cdot11} = \sqrt[3]{8}\cdot\sqrt[3]{11} = 2\sqrt[3]{11}[/tex]
4.
[tex]3\sqrt{7} = \sqrt{3^{2}\cdot7} = \sqrt{9\cdot7} = \sqrt{63}\\\\2\sqrt{10} = \sqrt{2^{2}\cdot10} = \sqrt{4\cdot10} = \sqrt{40}\\\\5\sqrt[3]{2} = \sqrt[3]{5^{3}\cdot2} = \sqrt[3]{125\cdot2} = \sqrt[3]{250}[/tex]
5.
[tex]2\sqrt{98}:\sqrt{2} =2\sqrt{98:2} = 2\sqrt{49} =2\sqrt{7^{2}}= 2\cdot7 = 14\\\\\sqrt{100-36} = \sqrt{64} = \sqrt{8^{2}} = 8\\\\\frac{\sqrt{32}+\sqrt{2}}{\sqrt{2}} =\frac{\sqrt{16\cdot2}+\sqrt{2}}{\sqrt{2}} = \frac{4\sqrt{2}+\sqrt{2}}{\sqrt{2}} = \frac{5\sqrt{2}}{\sqrt{2}} = 5\\\\\sqrt{3}(4\sqrt{3}-\sqrt{3}) =4\sqrt{3\cdot3} -\sqrt{3\cdot3} = 4\cdot3-3 = 12-3 = 9[/tex]
6.
[tex]\frac{3}{\sqrt{5}} = \frac{3}{\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}} = \frac{3\sqrt{5}}{5}\\\\\frac{12}{7\sqrt{2}}=\frac{12}{7\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{12\sqrt{2}}{7\cdot2} = \frac{12\sqrt{2}}{14} = \frac{6\sqrt{2}}{7}\\\\\frac{-3\sqrt{2}}{\sqrt{6}} = -3\sqrt{\frac{2}{6}} = -3\sqrt{\frac{1}{3}} = \frac{-3}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = \frac{-3\sqrt{3}}{3} =-\sqrt{3}[/tex]
