Find the geometric mean each pair of numbers. If nessary, give the answer in simplest radical form.

5 and 8

To find the geometric mean of a pair of numbers, you need to take the square root of their product.

So, for the pair of numbers 5 and 8, you would first find their product: 5 * 8 = 40.

Next, take the square root of their product to find the geometric mean: √40.

Now, let's simplify this radical expression. Start by determining if there are any perfect square factors of 40. In this case, 10 is a perfect square that can be extracted from 40 since 10 * 10 = 100.

So, rewrite 40 as the product of 10 and 4: 40 = 10 * 4.

Now, simplify the radical expression: √(10 * 4) = √10 * √4 = 2√10.

Therefore, the geometric mean of 5 and 8 is 2√10.