The geometric mean of 3, 5, and 6 is
A) 9.49.
B) 2.41.
C) 4.48.
D) 3.74.

Question

Quizplus · Accepted Answer

The geometric mean of three numbers $a$, $b$, and $c$ is $\sqrt[3]{abc}$. Thus, the geometric mean of 3, 5, and 6 is $\sqrt[3]{3\cdot5\cdot6}=\sqrt[3]{90}$. To approximate this value, we note that $4^3=64$ and $5^3=125$, so the cube root of 90 is between 4 and 5. Thus, we can approximate $\sqrt[3]{90}$ by finding the average of 4 and 5, which is 4.5. To refine our approximation, we note that $4.5^3=4^3\cdot5\cdot	frac12$, so $\sqrt[3]{90}$ is slightly less than 4.5. We can then use our calculator to find that $\sqrt[3]{90}\approx 4.48$. Thus, the answer is $\boxed{	extbf{(C)}}$.

The Geometric Mean of 3, 5, and 6 Is