#### Question

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

100^2 and 101^2

999^2 and 1000^2

11^2 and 12^2

Question

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

100^2 and 101^2

999^2 and 1000^2

11^2 and 12^2

The numbers between squares of two consecutive numbers are all non-perfect squares.

100^2 and 101^2

101^2-100^2 = (101-100)(101+100) = 201

Therefore, there are 200 non-square numbers between 100^2 and 101^2

999^2 and 1000^2

1000^2-999^2=(1000-999)(1000+999) = 1999

Therefore, there are 1998 non-square numbers between 999^2 and 1000^2

11^2 and 12^2

12^2-11^2 =(12-11)(12+11) = 23

Therefore, there are 22 non-square numbers between 11^2 and 12^2