# How do you find two geometric means between 4 and 64?

##### 1 Answer

Nov 28, 2015

Find a geometric sequence

#a = 8root(3)(2)#

#b = 16root(3)(4)#

#### Explanation:

We are effectively being asked to find

If the common ratio is

#a = 4r#

#b = ar = 4r^2#

#64 = br = 4r^3#

So

The only Real solution to this is

#a = 4r = 8root(3)(2)#

#b = ar = 8root(3)(2) * 2root(3)(2) = 16root(3)(4)#

Then

The other possible common ratios that work are