Find the geometric means of the following pairs of numbers:
Find the geometric means of the following pairs of numbers:

(i) 2 and 8
(ii) a3b and ab3

Solution:

(i) 2 and 8

According to the question, GM between a and b is √ab

We have a = 2 and b =8

GM = √2×8 = √16

GM = 4

(ii) a3b and ab3

According to the question, GM between a and b is √ab

We have a = a3b and b = ab3

GM = √(a3b × ab3) = √a4b4

GM = a2b2