거듭제곱근 대소 비교

[출제의도] 제곱근의 성질 이해하기 $\displaystyle \mathrm{A} = \sqrt[3]{\frac{1}{4}} = \left( \frac{1}{4} \right) ^{\frac{1}{3}} = \left( \frac{1}{4} \right) ^{\frac{4}{12}} = \left( \frac{1}{256} \right) ^{\frac{1}{12}}$ $\displaystyle \mathrm{B} = \sqrt[4]{\frac{1}{6}} = \left( \frac{1}{6} \right) ^{\frac{1}{4}} = \left( \frac{1}{6} \right) ^{\frac{3}{12}} = \left( \frac{1}{216} \right) ^{\frac{1}{12}}$ $\displaystyle \mathrm{C} = \sqrt[3]{\sqrt{\frac{1}{15}}} = \left( \frac{1}{15} \right) ^{\frac{2}{12}} = \left( \frac{1}{225} \right) ^{\frac{1}{12}}$ $\therefore$ $\mathrm{A} < C < B$