Question

Find the geometric mean of 6 and 7.

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) 
$m= \frac{a+b+c}{n}$
(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)$m_{geometric} = \sqrt[n]{a*b}$
$m_{geometric} = \sqrt{a*b}$
$m_{geometric} = \sqrt{6*7}$
$m_{geometric} = \sqrt{42}$

So the answer in this case is A.$\sqrt{42}$