Question

Find the geometric mean between 7 & 11. Select one:

a. 4√6 or appx. 9.8
b. 170/18 or appx 9.4
c. √77 or appx. 8.8
d. 9

Answer 1

The geometric mean is a variation on the standard arithmetic mean (where the numbers are totalled, then divided by the amount totalled). The latter of these two can be generalised as:


`(a_(1) + a_(2) + a_(3) ... + a_(n))/(n)`

The difference with a geometric mean is that instead of totalling the numbers, the product is found; similarly instead of a division stage at the end, an appropriate root is found:


`sqrt[n]({a_(1)a_(2)a_(3)...a_(n)})`

Therefore for this question n = 2, since there are two numbers. Substituting in:


`sqrt{7 * 11}` =
`√(77)` = 8.77496438739 ≈ 8.8 (2sf)