Question

The triplicate ratio of $\sqrt[3]{39}:\sqrt{8}$ is ____

• A. $9:16$
• B. $9:16\sqrt{2}$
• C. $9:8$
• D. $3:2$

Answer 1

Answer: (B)

$9:16\sqrt{2}$

$\sqrt[3]{39}:\sqrt{8}=(9{)}^{\frac{1}{3}}:(8{)}^{\frac{1}{2}}$
The triplicate ratio of $a:b$ is $a^3:b^3$
$\therefore$ The triplicate ratio of $\sqrt[3]{39}:\sqrt{8}$ is $\left[\right(9{)}^{\frac{1}{3}}{]}^3:\left[\right(8{)}^{\frac{1}{2}}{]}^3$
$=9:(2\sqrt{2}{)}^3$
$=9:8(\sqrt{2}{)}^3$
$=9:16\sqrt{2}$.