거듭제곱 대소 비교 빈칸

다음은 $\displaystyle {\sqrt{2}} ^{\sqrt{3}} \times {\sqrt{3}} ^{\sqrt{2}}$과 $\displaystyle {\sqrt{2}} ^{\sqrt{2}} \times {\sqrt{3}} ^{\sqrt{3}}$의 대소 관계를 알아보는 과정이다.

$\displaystyle {\sqrt{2}} ^{\sqrt{3}} \times {\sqrt{3}} ^{\sqrt{2}} - {\sqrt{2}} ^{\sqrt{2}} \times {\sqrt{3}} ^{\sqrt{3}}$ $\displaystyle = \sqrt{2} ^{\square {( \text{가} )}} \times \sqrt{3} ^{\sqrt{2}} \left( \sqrt{2} ^{\sqrt{3} - \sqrt{2}} - \sqrt{3} ^{\square {( \text{나} )}} \right)$ 그런데 $\displaystyle \sqrt{2} ^{\sqrt{3} - \sqrt{2}} \square {( \text{다} )} \sqrt{3} ^{\square {( \text{나} )}}$ 이고 $\displaystyle \sqrt{2} ^{\square {( \text{가} )}} > 0$, $\displaystyle {\sqrt{3}} ^{\sqrt{2}} > 0$ 이므로 $\displaystyle \sqrt{2} ^{\sqrt{3}} \times \sqrt{3} ^{\sqrt{2}} - \sqrt{2} ^{\sqrt{2}} \times \sqrt{3} ^{\sqrt{3}} \square {( \text{다} )} 0$ ∴ $\displaystyle \sqrt{2} ^{\sqrt{3}} \times \sqrt{3} ^{\sqrt{2}} \square {( \text{다} )} \sqrt{2} ^{\sqrt{2}} \times \sqrt{3} ^{\sqrt{3}}$

위의 과정에서 (가), (나), (다)에 알맞은 것은? [3점] (가) (나) (다) ①$\displaystyle \sqrt{2}$ $\displaystyle \sqrt{3} - \sqrt{2}$ $<$②$\displaystyle \sqrt{2}$ $\displaystyle \sqrt{3} - \sqrt{2}$ $>$③$\displaystyle \sqrt{2}$ $\displaystyle \sqrt{2} - \sqrt{3}$ $<$④$\displaystyle \sqrt{3}$ $\displaystyle \sqrt{2} - \sqrt{3}$ $>$⑤$\displaystyle \sqrt{3}$ $\displaystyle \sqrt{2} - \sqrt{3}$ $<$