有一根式，有理化之，使其分母無根式也。
3 6 = 3 6 × 6 6 = 3 6 6 = 6 2 {\displaystyle {\frac {3}{\sqrt {6}}}={\frac {3}{\sqrt {6}}}\times {\frac {\sqrt {6}}{\sqrt {6}}}={\frac {3{\sqrt {6}}}{6}}={\frac {\sqrt {6}}{2}}}
4 3 − 5 = 4 3 − 5 × 3 + 5 3 + 5 = 4 ( 3 + 5 ) 4 = 3 + 5 {\displaystyle {\frac {4}{3-{\sqrt {5}}}}={\frac {4}{3-{\sqrt {5}}}}\times {\frac {3+{\sqrt {5}}}{3+{\sqrt {5}}}}={\frac {4(3+{\sqrt {5}})}{4}}=3+{\sqrt {5}}}
1 x + y = 1 x + y × x − y x − y = x − y x − y {\displaystyle {\frac {1}{{\sqrt {x}}+{\sqrt {y}}}}={\frac {1}{{\sqrt {x}}+{\sqrt {y}}}}\times {\frac {{\sqrt {x}}-{\sqrt {y}}}{{\sqrt {x}}-{\sqrt {y}}}}={\frac {{\sqrt {x}}-{\sqrt {y}}}{x-y}}}
