Question

Find the geometric mean of 4 and 10

Answer 1

The geometric mean of 4 and 10 is 6.32.

Step-by-step explanation:

The geometric mean is a measure of central tendency calculated by multiplying a set of numbers and then taking the nth root, where n is the number of values. It is useful for finding the average in situations involving rates, ratios, and exponential growth.

The geometric mean of 4 and 10 is calculated by taking the square root of their product.

In this case, the product of 4 and 10 is 40.

Taking the square root of 40 gives us the geometric mean, which is approximately 6.32.

Therefore, the geometric mean of 4 and 10 is 6.32.

Answer 2

ANSWER


`Geometric \: \: Mean=2 √(10)`

EXPLANATION

The geometric mean for two real numbers,
x and y, where

`xy \geqslant 0`
is by


`Geometric \: \: Mean= √(xy)`

We apply this formula to find the geometric mean of 4 and 10 to be,


`Geometric \: \: Mean= √(4 * 10)`


`Geometric \: \: Mean= √(4) * √(10)`


`Geometric \: \: Mean=2 √(10)`

Or


`Geometric \: \: Mean=6.3` to the nearest tenth.