Pierwsze dwa przykłady
[tex]\frac{7}{\sqrt{11}}=\frac{7}{\sqrt{11}}\cdot\frac{\sqrt{11}}{\sqrt{11}}=\frac{7\sqrt{11}}{\sqrt{11^2}}=\frac{7\sqrt{11}}{11}\\\\\frac{3}{\sqrt[3]4}=\frac{3}{\sqrt[3]4}\cdot\frac{\sqrt[3]{4^2}}{\sqrt[3]{4^2}}=\frac{3\sqrt[3]{16}}{\sqrt[3]{4^3}}=\frac{3\sqrt[3]{8\cdot2}}{4}=\frac{3\cdot2\sqrt[3]2}{4}=\frac{6\sqrt[3]2}{4}=\frac{3\sqrt[3]2}{2}[/tex]
Kolejne dwa przykłady
[tex]\frac{1}{\sqrt7+\sqrt3}=\frac{1}{\sqrt7+\sqrt3}\cdot\frac{\sqrt7-\sqrt3}{\sqrt7-\sqrt3}=\frac{\sqrt7-\sqrt3}{(\sqrt7)^2-(\sqrt3)^2}=\frac{\sqrt7-\sqrt3}{7-3}=\frac{\sqrt7-\sqrt3}{4}\\\\\frac{1+\sqrt3}{3\sqrt5-1}=\frac{1+\sqrt3}{3\sqrt5-1}\cdot\frac{3\sqrt5+1}{3\sqrt5+1}=\frac{3\sqrt5+1+3\sqrt{15}+\sqrt3}{(3\sqrt5)^2-1^2}=\frac{3\sqrt5+3\sqrt{15}+\sqrt3+1}{45-1}=\frac{3\sqrt5+3\sqrt{15}+\sqrt3+1}{44}[/tex]
