Question

Simplifique a expressão $\frac{\sqrt[3]{0,25}-\sqrt[3]{2}}{\frac{3}{2}}$

Answer 1

Olá!

$\frac{\sqrt[3]{0,25}-\sqrt[3]{2}}{\frac{3}{2}}$
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$= \frac{ \sqrt[3]{ \frac{1}{4} } - \sqrt[3]{2} }{ \frac{3}{2} } \\ \\ = \Big(\sqrt[3]{ \frac{1}{4} } - \sqrt[3]{2} \Big) \cdot \frac{2}{3} \\ \\ = \frac{2\sqrt[3]{ \frac{1}{4} } - 2\sqrt[3]{2}}{3} \\ \\ = \frac{2 \cdot \frac{1}{ \sqrt[3]{4} } - 2 \sqrt[3]{2} }{3} \\ \\ = \frac{ \frac{2}{ \sqrt[3]{4} } - 2 \sqrt[3]{2} }{3} \\ \\ = \frac{ \sqrt[3]{2} - 2 \sqrt[3]{3} }{3} \\ \\ = \frac{(1 - 2) \sqrt[3]{2} }{3} \\ \\ = - \frac{ \sqrt[3]{2} }{3}$


$\textbf{Bons estudos}$ !