#3**+10 **

The geometric mean only applies to positive numbers.

It has a geometric interpretation. Image a rectangle with sides 10 and 30. It has an area of 300. A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.

Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths ^{3}√(u*v*w), etc.

.

Alan
Feb 14, 2015

#1**+10 **

The geometric mean of N numbers is just the Nth root of their product.....so, since we have two numbers, we have....

√(10 * 30) = √300 = 10√3

CPhill
Feb 14, 2015

#2**+5 **

**SO**

The geometric mean of 7,6,8 and 2

is it $$\sqrt[4]{7*6*8*2}$$

$${\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}^{\left({\mathtt{0.25}}\right)} = {\mathtt{5.091\: \!459\: \!790\: \!043\: \!661}}$$

**what happen if there is negative numbers?**

Melody
Feb 14, 2015

#3**+10 **

Best Answer

The geometric mean only applies to positive numbers.

It has a geometric interpretation. Image a rectangle with sides 10 and 30. It has an area of 300. A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.

Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths ^{3}√(u*v*w), etc.

.

Alan
Feb 14, 2015