What is the geometric mean of 5 and 15?

2 Answers
Jan 29, 2016

#5sqrt(3)#

Explanation:

If you have say 3 variables : a; b; c

Then the Geometric mean for these 3 numbers is:

#root(3)(axxbxxc)#

Then for any variable #x_i#

#root(n)(x_1xxx_2xx...xx x_ixx ...xxx_n) #

So for your numbers:

#root(2)(5xx15) = sqrt(75)#

#sqrt( 5^2xx3)=5sqrt(3)#

Feb 14, 2018

#8.66#

Explanation:

In a GP, there is always a constant ratio between consecutive terms.

So for a sequence #a , b, c" "rarr c/b = b/a#

#b# is called the geometric mean.

So for the sequence #5, x, 15" "rarr 15/x = x/5#

Cross multiplying gives us:

#x^2 = 15xx5 #

#x^2 = 75#

#x = sqrt75#

#x = 8.66#