Question

The geometric mean of $2,6,8,24$ is

• A. $\sqrt{48}=4\sqrt{3}$
• B. $16$
• C. $24$
• D. $36$

Answer 1

The correct option is A $\sqrt{48}=4\sqrt{3}$

Geometric Mean of $n$ terms is $(\text{Product of Terms}{)}^{\frac{1}{n}}$

$\therefore$ Geometric Mean $=(2\times 6\times 8\times 24{)}^{\frac{1}{4}}$
$=(2^8\times 3^2{)}^{\frac{1}{4}}$ $=2^2\times 3^{\frac{1}{2}}$
$=4\sqrt{3}=\sqrt{48}$