The Geometric mean is a special type of mean where we multiply the numbers together and also then take it a square source (for two numbers), cube root (for 3 numbers) etc.

You are watching: Geometric mean of 8 and 12

### Example: What is the Geometric mean of 2 and also 18?

First we multiply them: 2 × 18 = 36Then (as there space two numbers) take it the square root: √36 = 6

In one line:

Geometric mean of 2 and also 18 = √(2 × 18) = 6

It is favor the area is the same!

### Example: What is the Geometric typical of 10, 51.2 and also 8?

First we multiply them: 10 × 51.2 × 8 = 4096Then (as there are three numbers) take it the cube root: 3√4096 = 16

In one line:

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

It is prefer the volume is the same:

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

First us multiply them: 1 × 3 × 9 × 27 × 81 = 59049Then (as there room 5 numbers) take the fifth root: 5√59049 = 9

In one line:

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

I can"t display you a nice snapshot of this, yet it is quiet true that:

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

### Example: What is the Geometric mean of a Molecule and a Mountain

Using clinical notation:

A molecule that water (for example) is 0.275 × 10-9 mMount Everest (for example) is 8.8 × 103 m

### Example: you want to buy a new camera.

One camera has actually a zoom that 200 and gets an 8 in reviews,The other has a zoom that 250 and gets a 6 in reviews.

Comparing making use of the usual arithmetic mean provides (200+8)/2 = 104 vs (250+6)/2 = 128. The zoom is such a big number the the user rating gets lost.

But the geometric way of the 2 cameras are:

√(200 × 8) = 40√(250 × 6) = 38.7...

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So, even though the zoom is 50 bigger, the lower user rating the 6 is still important.