Find the geometric means of the following pairs of numbers :
i. 2 and 8
ii. a3b and ab3
iii. –8 and –2
(i) GM = √ab
Let a = 2 and b =8
GM = √2×8
= √16
= 4.
(ii) GM = √xy
Let x = a3b and y = ab3
GM = √ a3b × ab3
= √a4b4
= a2b2.
(iii) GM = √ab
Let a = –2 and b = –8
GM = √–2×–8
= √–16
[we know that √–1 = i(iota)]
= 4i.