Find the duplicate ratio of $2\sqrt{2} : 3\sqrt{5}$

Duplicate ratio of $2\sqrt{2} : 3\sqrt{5}$,

$= (2\sqrt{2})^2 : (3\sqrt{5})^2 \\[1em] = 8 : 45.$

Hence, duplicate ratio of $2\sqrt{2} : 3\sqrt{5}$ = 8 : 45.