How many numbers lie between squares of the following numbers?
(i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100
Since between n2 and (n + l)2, there are 2n non-square numbers.
∴ (i) Between 122 and 132, there are 2 × 12, i.e. 24 numbers
(ii) Between 252 and 26:, there are 2 × 25, i.e. 50 numbers
(iii) Between 992 and 1002, there are 2 × 99, i.e. 198 numbers
