Ensino Fundamental ⇒ (EPCAR) Racionalização Tópico resolvido

[erastóstones]

Racionalizando o denominador da expressão abaixo

[tex3]\frac{1}{\sqrt[3]{2}+1}[/tex3]

[AlexandreHDK]

[tex3]\frac{1}{\sqrt[3]{2}+1}=\frac{1}{\sqrt[3]{2}+1}.\frac{(\sqrt[3]{2})^2-\sqrt[3]{2}+1}{(\sqrt[3]{2})^2-\sqrt[3]{2}+1}=\frac{(\sqrt[3]{2})^2-\sqrt[3]{2}+1}{\sqrt[3]{2}.(\sqrt[3]{2})^2-\sqrt[3]{2}.\sqrt[3]{2}+\sqrt[3]{2}+(\sqrt[3]{2})^2-\sqrt[3]{2}+1}[/tex3]
[tex3]=\frac{(\sqrt[3]{2})^2-\sqrt[3]{2}+1}{(\sqrt[3]{2})^3-\cancel{(\sqrt[3]{2})^2}+\cancel{\sqrt[3]{2}}+\cancel{(\sqrt[3]{2})^2}-\cancel{\sqrt[3]{2}}+1}[/tex3]
[tex3]=\frac{(\sqrt[3]{2})^2-\sqrt[3]{2}+1}{(\sqrt[3]{2})^3-1}=\frac{(\sqrt[3]{2})^2-\sqrt[3]{2}+1}{2-1}=(\sqrt[3]{2})^2-\sqrt[3]{2}+1[/tex3]