Question

Qual o resultado da seguinte divisão?

Answer 1

$\dfrac{1}{\sqrt[3]{4+2\sqrt{2}} \times \sqrt[3]{4-2\sqrt{2}} }\\\\\\ =\dfrac{1}{\sqrt[3]{(4+2\sqrt{2})(4-2\sqrt{2})}}\\\\\\ =\dfrac{1}{\sqrt[3]{16-8\sqrt{2}+8\sqrt{2}-4\sqrt{2^2}}}\\\\\\ =\dfrac{1}{\sqrt[3]{16-4(2)}}\\\\\\ =\dfrac{1}{\sqrt[3]{16-8}}\\\\\\ =\dfrac{1}{\sqrt[3]{8}}\\\\\\ =\dfrac{1}{\sqrt[3]{2 \times 2 \times 2}}\\\\\\ =\dfrac{1}{\not\sqrt[3]{2^{\not3}}}\\\\\\ \boxed{=\dfrac{1}{2}=0,5}$

Bons estudos!