Question

Find the geometric means of the following pairs of numbers :

i. 2 and 8

ii. a³b and ab³

iii. –8 and –2

Answer 1

(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.