[tex]zad.1\\\\a)\\\\\dfrac{5}{\sqrt{2} } =\dfrac{5}{\sqrt{2} } \cdot \dfrac{\sqrt{2} }{\sqrt{2} } =\dfrac{5\sqrt{2} }{\sqrt{2}\cdot \sqrt{2} } =\dfrac{5\sqrt{2} }{\sqrt{4} } =\dfrac{5\sqrt{2} }{2} \\\\b)\\\\\dfrac{6}{\sqrt[3]{9} } =\dfrac{6}{\sqrt[3]{9} }\cdot \dfrac{\sqrt[3]{3} }{\sqrt[3]{3} } =\dfrac{6\sqrt[3]{3} }{\sqrt[3]{3^{2} } \cdot \sqrt[3]{3} } =\dfrac{6\sqrt[3]{3} }{\sqrt[3]{3^{2} \cdot 3} } =\dfrac{6\sqrt[3]{3} }{\sqrt[3]{3^{3}} } =\dfrac{6\sqrt[3]{3} }{3} =2\sqrt[3]{3} \\\\zad.2\\\\[/tex]
[tex]a)\\\\5\sqrt{3}=\sqrt{5^{2} \cdot 3} =\sqrt{25\cdot 3} =\sqrt{75} \\\\b)\\\\\dfrac{1}{2} \sqrt{6} =\sqrt{(\dfrac{1}{2} )^{2} \cdot 6} =\sqrt{\dfrac{1}{4} \cdot 6} =\sqrt{\dfrac{6}{4} } =\sqrt{\dfrac{3}{2} }\\\\zad.3\\\\c)\\\\\sqrt[3]{80} =\sqrt[3]{8\cdot 10} =\sqrt[3]{2^{3} \cdot 10} =\sqrt[3]{2^{3} } \cdot \sqrt[3]{10} =2^{3\cdot \frac{1}{3} } \cdot \sqrt[3]{10} = 2\sqrt[3]{10}[/tex]
korzystałam ze wzorów:
[tex]x=\sqrt[n]{x^{n} } =x^{n\cdot \frac{1}{n} } \\\\\sqrt[n]{x\cdot y} =\sqrt[n]{x} \cdot \sqrt[n]{y}[/tex]