Question

Racionalize as expressões:

Answer 1

a) $\frac{8}{\sqrt{6}}=\frac{8}{\sqrt{6}}.\frac{\sqrt{6}}{\sqrt{6}}=\frac{8\sqrt{6}}{\sqrt{6}\sqrt{6}}=\frac{8\sqrt{6}}{6}=\frac{4\sqrt{6}}{3}$

b) $\frac{4}{\sqrt[5]{2^3}}=\frac{4}{\sqrt[5]{2^3}}.\frac{\sqrt[5]{2^2}}{\sqrt[5]{2^2}}=\frac{4\sqrt[5]{2^2}}{\sqrt[5]{2^3}\sqrt[5]{2^2}}=\frac{4\sqrt[5]{2^2}}{\sqrt[5]{2^3.2^2}}=\frac{4\sqrt[5]{2^2}}{\sqrt[5]{2^5}}=\frac{4\sqrt[5]{2^2}}{2}=2\sqrt[5]{2^2}=2\sqrt[5]{4}$

c) $\frac{1}{\sqrt{3}+4}=\frac{1}{\sqrt{3}+4 }.\frac{\sqrt{3}-4}{\sqrt{3}-4}=\frac{1(\sqrt{3}-4)}{(\sqrt{3}+4).(\sqrt{3}-4)}=\frac{\sqrt{3}-4}{3-16}=\frac{\sqrt{3}-4}{-13}=-\frac{\sqrt{3}-4}{13}$