Question

What are the geometric means of \( x \) and \( y \)?

Hint:

The geometric mean is used to find the central tendency of multiplicative values. Always use \( \sqrt{xy} \) to calculate the geometric mean.

Answer 1

Step 1: Understanding the formula for the geometric mean.
The geometric mean of two numbers \( x \) and \( y \) is calculated as the square root of their product. This is given by: \[ A = \sqrt{xy} \] Thus, option A correctly represents the geometric mean of \( x \) and \( y \).
Step 2: Explanation of the alternatives.
- B and C: While B and C express different forms such as \( x \cdot y \), the standard and most widely accepted formula for the geometric mean is A.
Step 3: Additional Expression.
The second part of the question shows the expression: \[ \sqrt{\frac{m^2 - d^2}{4}} \] This formula seems to be related to a different calculation, possibly involving distance or other geometric concepts, but it is not directly linked to the geometric mean of \( x \) and \( y \).
Step 4: Conclusion.
The correct geometric mean formula is \( A \), i.e., \( \sqrt{xy} \).