9.How many numbers lie between squares of the following numbers?
(i) 12 and 13

(ii) 25 and 26

(iii) 99 and 100.

We know that numbers between \(n^2\) and \((n + 1)^2\) = 2n

(i) Numbers between \(12^2\) and \(13^2\) = (2n) = \(2 \times 12\) = 24

(ii) Numbers between \(25^2\) and \(26^2\) = \(2 \times 25\) = 50 [ n = 25]

(iii) Numbers between \(99^2\) and \(100^2\) = \(2 \times 99\) = 198 [ n = 99]