What is the geometric mean of 2, 4, and 8?
Show Hint
- 4.67
- 3.43
- 4
- 4.5
The Correct Option is B
Solution and Explanation
Step 1: Formula for geometric mean.
The geometric mean of \( n \) values \( x_1, x_2, \dots, x_n \) is given by:
\[
GM = \left( \prod_{i=1}^n x_i \right)^{\frac{1}{n}}
\]
Step 2: Apply the formula.
For the values 2, 4, and 8, the geometric mean is:
\[
GM = (2 \cdot 4 \cdot 8)^{\frac{1}{3}}
\]
\[
GM = (64)^{\frac{1}{3}} = 4
\]
Step 3: Conclusion.
The geometric mean of 2, 4, and 8 is 4, so the correct answer is (C).
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