if one numbers is 6 and the geometric mean of the two numbers is 4. What is the other number?

Answer 1

Hello, Rashel,

The geometric mean of two numbers is the square root of their product. 6 is one number and we'll say the other number is X.

The product is 6*X, We know the square root of this value is 4, the remetric mean.

(6*X)^1/2 = 4

6*X = 16

X = (16/6), or (8/3).

This sounds awful - who needs fractions like this in their life? But let's see if it works:

(6*(8/3))^1/2

(2*8)^1/2

(16)^1/2 = 4

It seems to work,

Bob

Answer 2

the other number is 8/3

sqr6x = 4

square both sides to get

6x = 16

x = 16/6 = 8/3 = 2 2/3 = 2.666....