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.


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