Ensino Fundamental ⇒ Simplificação de radicais Tópico resolvido

[engenheirita]

[tex3]\left(\frac{\sqrt{8}+\sqrt[3]{12}+\sqrt[4]{4}}{\sqrt{2}}\right)[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\left(\frac{\sqrt{8}+\sqrt[3]{12}+\sqrt[4]{4}}{\sqrt{2}}\right)[/tex3]

Alguém pode resolver passo a passo, por favor?


gab

Resposta

---

3+[tex3]\sqrt[6]{18}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\sqrt[6]{18}[/tex3]

[petras]

[tex3]\mathsf{\left(\frac{\sqrt{8}+\sqrt[3]{12}+\sqrt[4]{4}}{\sqrt{2}}\right)=\\
\left(\frac{2\sqrt{2}+\sqrt[3]{12}+\sqrt[]{2}}{\sqrt{2}}\right)=\\
\left(\frac{3\sqrt{2}+\sqrt[3]{12}}{\sqrt{2}}\right)=\\
3+[\frac{2^{\frac{1}{3}}.6^{\frac{1}{3}}}{2^{\frac{1}{2}}}]=3 + [\frac{2^\frac{1}{3}2^\frac{1}{3}.3^\frac{1}{3}}{2^\frac{1}{2}}]=3 + 2 ^\frac{1}{6}.3^{\frac{1}{3}}=3 + [\sqrt[6]{2}.\sqrt[3]{3}]=\\3 + [\sqrt[6]{2}.\sqrt[6]{3^2}]=\boxed{\mathsf{\color{red}3+\sqrt[6]{18}}}
}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\mathsf{\left(\frac{\sqrt{8}+\sqrt[3]{12}+\sqrt[4]{4}}{\sqrt{2}}\right)=\\
\left(\frac{2\sqrt{2}+\sqrt[3]{12}+\sqrt[]{2}}{\sqrt{2}}\right)=\\
\left(\frac{3\sqrt{2}+\sqrt[3]{12}}{\sqrt{2}}\right)=\\
3+[\frac{2^{\frac{1}{3}}.6^{\frac{1}{3}}}{2^{\frac{1}{2}}}]=3 + [\frac{2^\frac{1}{3}2^\frac{1}{3}.3^\frac{1}{3}}{2^\frac{1}{2}}]=3 + 2 ^\frac{1}{6}.3^{\frac{1}{3}}=3 + [\sqrt[6]{2}.\sqrt[3]{3}]=\\3 + [\sqrt[6]{2}.\sqrt[6]{3^2}]=\boxed{\mathsf{\color{red}3+\sqrt[6]{18}}}
}[/tex3]

[engenheirita]

[tex3]\mathsf{\left(\frac{\sqrt{8}+\sqrt[3]{12}+\sqrt[4]{4}}{\sqrt{2}}\right)=\\
\left(\frac{2\sqrt{2}+\sqrt[3]{12}+\sqrt[]{2}}{\sqrt{2}}\right)=\\
\left(\frac{3\sqrt{2}+\sqrt[3]{12}}{\sqrt{2}}\right)=\\
3+[\frac{2^{\frac{1}{3}}.6^{\frac{1}{3}}}{2^{\frac{1}{2}}}]=3 + [\frac{2^\frac{1}{3}2^\frac{1}{3}.3^\frac{1}{3}}{2^\frac{1}{2}}]=3 + 2 ^\frac{1}{6}.3^{\frac{1}{3}}=3 + [\sqrt[6]{2}.\sqrt[3]{3}]=\\3 + [\sqrt[6]{2}.\sqrt[6]{3^2}]=\boxed{\mathsf{\color{red}3+\sqrt[6]{18}}}
}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\mathsf{\left(\frac{\sqrt{8}+\sqrt[3]{12}+\sqrt[4]{4}}{\sqrt{2}}\right)=\\
\left(\frac{2\sqrt{2}+\sqrt[3]{12}+\sqrt[]{2}}{\sqrt{2}}\right)=\\
\left(\frac{3\sqrt{2}+\sqrt[3]{12}}{\sqrt{2}}\right)=\\
3+[\frac{2^{\frac{1}{3}}.6^{\frac{1}{3}}}{2^{\frac{1}{2}}}]=3 + [\frac{2^\frac{1}{3}2^\frac{1}{3}.3^\frac{1}{3}}{2^\frac{1}{2}}]=3 + 2 ^\frac{1}{6}.3^{\frac{1}{3}}=3 + [\sqrt[6]{2}.\sqrt[3]{3}]=\\3 + [\sqrt[6]{2}.\sqrt[6]{3^2}]=\boxed{\mathsf{\color{red}3+\sqrt[6]{18}}}
}[/tex3]

Muito obrigada!