Question

11. The geometric mean of two numbers is 2. Find a number 4 times the other number.​

Answer 1

Answer:

Example: What is the Geometric Mean of 2 and 18?

First we multiply them: 2 × 18 = 36

Then (as there are two numbers) take the square root: √36 = 6

In one line:

Geometric Mean of 2 and 18 = √(2 × 18) = 6

It is like the area is the same!

geometric mean 2x18 = 6x6

Example: What is the Geometric Mean of 10, 51.2 and 8?

First we multiply them: 10 × 51.2 × 8 = 4096

Then (as there are three numbers) take the cube root: 3√4096 = 16

In one line:

Geometric Mean = 3√(10 × 51.2 × 8) = 16

It is like the volume is the same:

geometric mean 10x51.2x8 = 16x16x16

Example: What is the Geometric Mean of 1, 3, 9, 27 and 81?

First we multiply them: 1 × 3 × 9 × 27 × 81 = 59049

Then (as there are 5 numbers) take the 5th root: 5√59049 = 9

In one line:

Geometric Mean = 5√(1 × 3 × 9 × 27 × 81) = 9

I can't show you a nice picture of this, but it is still true that:

1 × 3 × 9 × 27 × 81 = 9 × 9 × 9 × 9 × 9