Odpowiedź:
[tex]a)\ \ \dfrac{2\sqrt{2}}{\sqrt{5}}-\dfrac{5}{\sqrt{10}}=\dfrac{2\sqrt{2}}{\sqrt{5}}*\dfrac{\sqrt{5}}{\sqrt{5}}-\dfrac{5}{\sqrt{10}}*\dfrac{\sqrt{10}}{\sqrt{10}}=\dfrac{2\sqrt{10}}{5}-\dfrac{5\sqrt{10}}{10}=\dfrac{2*2\sqrt{10}}{10}-\dfrac{5\sqrt{10}}{10}\\\\\\=\dfrac{4\sqrt{10}}{10}-\dfrac{5\sqrt{10}}{10}=-\dfrac{\sqrt{10}}{10}[/tex]
[tex]b)\ \ \dfrac{\sqrt{2}}{\sqrt{3}}+\dfrac{4}{\sqrt{6}}=\dfrac{\sqrt{2}}{\sqrt{3}}*\dfrac{\sqrt{3} }{\sqrt{3}}+\dfrac{4}{\sqrt{6}}*\dfrac{\sqrt{6}}{\sqrt{6}}=\dfrac{\sqrt{6} }{3}+\dfrac{4\sqrt{6}}{6}=\dfrac{2\sqrt{6}}{6}+\dfrac{4\sqrt{6}}{6}=\\\\\\=\dfrac{\not6\sqrt{6}}{\not6}=\sqrt{6}[/tex]
[tex]c)\ \ \dfrac{4}{\sqrt[3]{10}}-\dfrac{2\sqrt[3]{4}}{\sqrt[3]{5}}=\dfrac{4}{\sqrt[3]{10}}*\dfrac{\sqrt[3]{10^2}}{\sqrt[3]{10^2}}-\dfrac{2\sqrt[3]{4}}{\sqrt[3]{5}}*\dfrac{\sqrt[3]{5^2}}{\sqrt[3]{5^2}}=\dfrac{4\sqrt[3]{10^2}}{\sqrt[3]{10*10^2}}-\dfrac{2\sqrt[3]{4*5^2}}{\sqrt[3]{5*5^2}}=\\\\\\=\dfrac{4\sqrt[3]{10^2}}{\sqrt[3]{10^3}}-\dfrac{2\sqrt[3]{4*5^2}}{\sqrt[3]{5^3}}=\dfrac{4\sqrt[3]{10^2}}{10}-\dfrac{2\sqrt[3]{4*25}}{5}=\dfrac{4\sqrt[3]{100}}{10}-\dfrac{4\sqrt[3]{100}}{10}=0[/tex]
[tex]d)\ \ \dfrac{8}{\sqrt[3]{4}}-\dfrac{2\sqrt[3]{4}}{\sqrt[3]{2}}=\dfrac{8}{\sqrt[3]{2^2}}-\dfrac{2*\sqrt[3]{2}*\sqrt[3]{2}}{\sqrt[3]{2}}=\dfrac{8}{\sqrt[3]{2^2}}*\dfrac{\sqrt[3]{2} }{\sqrt[3]{2}}-2\sqrt[3]{2}=\dfrac{8\sqrt[3]{2}}{\sqrt[3]{2^2*2}}-2\sqrt[3]{2}=\\\\\\=\dfrac{8\sqrt[3]{2}}{\sqrt[3]{2^3}}-2\sqrt[3]{2}=\dfrac{\not8^4\sqrt[3]{2}}{\not2_{1} }-2\sqrt[3]{2}=4\sqrt[3]{2}-2\sqrt[3]{2}=2\sqrt[3]{2}[/tex]
