How many numbers lie between squares of the following numbers? 

(i) 12 and 13

 (ii) 25 and 26 

(iii) 99 and 100

(i) 12 and 13

Here,

12² = 144 and 13² = 169

a = 144 and b = 169

b > a using, b-a-1

169-144-1 = 24 

There are 24 numbers between squares of numbers 12 and 13.

 (ii) 25 and 26 

Here,

25² = 625 and 26² = 676

a = 625 and b = 676

b > a using, b-a-1

676 - 625-1 = 50

There are 50 numbers between squares of numbers 25 and 26.

(iii) 99 and 100

Here,

99² = 9801 and 100² = 10000

a = 9801 and b = 10000

b > a using, b-a-1

10000 - 9801-1 = 198

There are 198 numbers between squares of numbers 99 and 100.