Question

Избавьтесь от иррациональности в дроби $\frac{2}{ \sqrt[3]{4} }$

Answer 1

$\displaystyle\bf\\\frac{2}{\sqrt[3]{4} } =\frac{2\cdot\sqrt[3]{2} }{\sqrt[3]{4} \cdot\sqrt[3]{2} } =\frac{2\cdot\sqrt[3]{2} }{\sqrt[3]{4\cdot2} }=\frac{2\cdot\sqrt[3]{2} }{\sqrt[3]{2^{3} } }=\frac{2\cdot\sqrt[3]{2} }{2}=\sqrt[3]{2}$

Answer 2

$\displaystyle \tt \frac{2}{ \sqrt[3]{4} } = \frac{2}{ \sqrt[3]{2 {}^{2} } } = \frac{2}{ \sqrt[3]{2 {}^{2} } } \cdot \frac{ \sqrt[3]{2} }{ \sqrt[3]{2} } = \frac{2 \sqrt[3]{2} }{ \sqrt[3]{2 {}^{2} } \sqrt[3]{2} } = \frac{2 \sqrt[3]{2} }{ \sqrt[3]{2 {}^{2} \cdot2 } } = \frac{2 \sqrt[3]{2} }{ \sqrt[3]{2 {}^{3} } } = \frac{ \not2 \sqrt[3]{2} }{ \not2} = \sqrt[3]{2} .$