Question

Find the geometric mean of 6 and 7.

A. √42

B. 4√3

C. 7

D. 42




Please select the best answer from the choices provided.

Answer 1

First, it is important to understand the terms used in the problem.

The Arithmetic Mean: (this is the mean we are used to seeing)

`m= (a+b+c)/(n)`
(n= number of variables, in this case n=3)

To Find the Geometric Mean of n #'s:

`m_(geometric) = \sqrt[n]{a*b}`
(n= number of variables, in this case n=2)


So, using this information we can find the geometric mean of 6,7 by plugging them into the equation as "a" and "b". n=2 (when n=2 a square root can be used)
`m_(geometric) = \sqrt[n]{a*b}`

`m_(geometric) = √(a*b)`

`m_(geometric) = √(6*7)`

`m_(geometric) = √(42)`

So the answer in this case is A.
`√(42)`