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 2*n* numbers in between the squares of the numbers *n* and (*n* + 1)

Now,

(i) Between 12^{2} and 13^{2}:

There will be 2 x 12

= 24 numbers

(ii) Between 25^{2} and 26^{2}:

there will be 2 x 25

= 50 numbers

(iii) Between 99^{2} and 100^{2}, there will be 2 x 99

= 198 numbers

14