Question

como faz?? nao tenho nenhuma ideia

Answer 1

Simplificar $\frac{\sqrt[3]{0,25}-\sqrt[3]{2}}{\sqrt[3]{2}}$

Temos que

$0,25=\frac{1}{4}=\frac{1}{2^{2}}$

Logo, podemos fazer a substituição

$\frac{\sqrt[3]{0,25}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\sqrt[3]{\frac{1}{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\frac{\sqrt[3]{1}}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\frac{1}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}} \rightarrow\,\,\left(\times \frac{\sqrt[3]{2^2}}{\sqrt[3]{2^2}}\right)\\ \\ =\frac{\left(\frac{1}{\sqrt[3]{2^{2}}}-\sqrt[3]{2} \right) \times \sqrt[3]{2^{2}}}{\sqrt[3]{2} \times \sqrt[3]{2^{2}}}\\ \\ =\frac{\frac{\sqrt[3]{2^{2}}}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}\times\sqrt[3]{2^{2}}}{\sqrt[3]{2} \times \sqrt[3]{2^{2}}}\\ \\ =\frac{1-\sqrt[3]{2^{3}}}{\sqrt[3]{2^{3}}}\\ \\ =\frac{1-2}{2}\\ \\ =\boxed{-\frac{1}{2}}$