Question

How many numbers lie between squares
the following numbers?
(1) 12 and 13 (ii) 25 and 26
(iii) 99 and 100
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Answer 1

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(i) We know that numbers between n2 and (n + 1)2 = 2n

Numbers between 122 and 132 = (2n) = 2 × 12 = 24

(ii) Numbers between 252 and 262 = 2 × 25 = 50 (∵ n = 25)

(iii) Numbers between 992 and 1002 = 2 × 99 = 198 (∵ n = 99)