Question

_____ is the subtriplicate ratio of $64:729$

• A. $729:64$
• B. $16:81$
• C. $4:9$
• D. $2:3$

Answer 1

Answer: (C)

$4:9$

The subtriplicate ratio of $a:b$ is $\sqrt[3]{3a}:\sqrt[3]{3b}$.
$\therefore$ The subtriplicate ratio of $64:729$ is $\sqrt[3]{364}=\sqrt[3]{3729}=\sqrt[3]{3(4{)}^3}:\sqrt[3]{3(9{)}^3}=4:9$.