Question

Racionalize os denominadores e marque a opção correta

Answer 1

I.

$\frac{7}{\sqrt{7}+2}\\\\\frac{7}{\sqrt{7}+2}.\frac{\sqrt{7}-2}{\sqrt{7}-2}\\\\\frac{7\;.\;(\sqrt{7}-2)}{\sqrt{7}^2+2\sqrt{7}-2\sqrt{7}-2^2}\\\\\frac{7(\sqrt{7}-2)}{7-4}\\\\\frac{7(\sqrt{7}-2)}{3}$

II.

$\frac{1}{\sqrt[5]{\sqrt{16}}}\\\\\frac{1}{\sqrt[5]{4}}\\\\\frac{1}{\sqrt[5]{4}}.\frac{\sqrt[5]{4}^4}{\sqrt[5]{4}^4}\\\\\frac{\sqrt[5]{4}^4}{\sqrt[5]{4}^5}\\\\\frac{\sqrt[5]{4^4}}{4}\\\\\frac{\sqrt[5]{256}}{4}$

III.

$\frac{7}{2\sqrt{3}}\\\\\frac{7}{2\sqrt{3}}.\frac{\sqrt{3}}{\sqrt{3}} \\\\\frac{7\sqrt{3}}{2.\sqrt{3}^2}\\\\\frac{7\sqrt{3}}{2\;.\;3}\\\\\frac{7\sqrt{3}}{6}$