Question

The geometric mean of numbers 10, 16, and 50 will be:

• A. 40
• B. 20
• C. 60
• D. 50

Hint:

The geometric mean is found by taking the \( n \)-th root of the product of \( n \) numbers.

Answer 1

The Correct Option is B

The geometric mean \( G \) of \( n \) numbers is given by the formula: \[ G = \sqrt[n]{x_1 \times x_2 \times \cdots \times x_n} \] where \( x_1, x_2, \ldots, x_n \) are the numbers. For the numbers 10, 16, and 50, the geometric mean is: \[ G = \sqrt[3]{10 \times 16 \times 50} \] First, calculate the product: \[ 10 \times 16 = 160 \] \[ 160 \times 50 = 8000 \] Now, calculate the cube root: \[ G = \sqrt[3]{8000} = 20 \] Thus, the geometric mean of 10, 16, and 50 is 20.