Verify that the geometric mean of 10 and 50 is a smaller than arithmetic mean.

 Verify that the geometric mean of 10 and 50 is a smaller than arithmetic mean.

Solutions

The geometric mean ($��$) of two numbers $�$ and $�$ is given by:

$��=\sqrt{��}$

The arithmetic mean ($��$) of two numbers $�$ and $�$ is given by:

$��=\frac{�+�}{2}$

For the given numbers 10 and 50:

$��=\sqrt{10\times 50}=\sqrt{500}\approx 22.36$

$��=\frac{10+50}{2}=30$

So, the geometric mean is approximately 22.36, and the arithmetic mean is 30. As the geometric mean is smaller than the arithmetic mean, the statement is verified.