How many numbers lie between squares of the following numbers?

(i) 12 and 13

(ii) 25 and 26

(iii) 99 and 100

We know:

There will be 2n numbers in between the squares of the numbers n and (n + 1)

Now,

(i) Between 12² and 13²:

There will be 2 x 12

= 24 numbers

(ii) Between 25² and 26²:

there will be 2 x 25

= 50 numbers

(iii) Between 99² and 100², there will be 2 x 99

= 198 numbers