How many non-square numbers lie between the following pairs of numbers:

(i) 100² and 101² (ii) 90² and 91²

(iii) 1000² and 1001²

(i) Between 100² and 101²
Here, n=100 ∴  n x2 = 100 x 2 = 200

∴ 200 non-square numbers lie between 100² and 101² .

(ii)  Between 90² and 91²

Here, n=90  ∴  2 x n = 2 x 90 or 180

∴  180 non-square numbers lie between 90 and 91.

(iii)  Between 1000² and 1001²

Here, n = 1000         ∴  2 x n = 2 x 1000 or 2000
∴  2000 non-square lie between 1000² and 10012.