What is the geometric mean of two positive numbers?

The geometric mean of two positive numbers is defined as the positive square root of the product of those two numbers. This concept is particularly useful in various fields, including geometry, finance, and statistics, as it provides a meaningful way to find an average rate of growth or a central tendency when dealing with proportions or ratios.

When you take two positive numbers, let's call them (a) and (b), the geometric mean can be expressed mathematically as (\sqrt{ab}). This means that you multiply the two numbers together to find their product and then take the square root of that product. Since both numbers are positive, the geometric mean will also be a positive number, which aligns with the requirement for the geometric mean.

In practical terms, the geometric mean would be more appropriate than the arithmetic mean (the average) in situations involving exponential growth or rates, such as population growth or interest rates. Therefore, when determining the geometric mean for any two positive numbers, the correct methodology is indeed to calculate the positive square root of their product.