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


21