Question

Racionalizando a fração $\boxed{ \frac{1}{ \sqrt[4]{4} - 1 }}$ obtemos:

A) $\sqrt{2} + 1.$

B) $\sqrt{2}-1.$

C) $\sqrt[4]{2}-1.$

D) $\sqrt[4]{2} +1 .$

E) $\sqrt[4]{2^3} .$

Divirtam-se. :))

Answer 1

$\boxed{\frac{1}{ \sqrt[4]{4} -1}=\frac{1}{ \sqrt[4]{2^2} -1}=\frac{1}{2^{\frac{2}{4}}-1}=\frac{1}{\sqrt2-1}.\frac{\sqrt2+1}{\sqrt2+1}=\frac{\sqrt2+1}{1}=\sqrt2+1}}$

Answer 2

$\frac{1}{ \sqrt[4]{4}-1} = \frac{1}{ \sqrt[4]{2^2}-1} =\frac{1}{2^{\frac{2}{4}} -1}= \frac{1}{2^{\frac{1}{2}}-1}= \frac{1}{\sqrt{2} -1} \\ \frac{1}{\sqrt{2}-1} .\frac{\sqrt{2}+1}{\sqrt{2}+1}=\frac{\sqrt{2}+1}{1}= \boxed{\sqrt{2}+1}}$