Question

How many non square numbers lie between 1000² and 1001
²

Answer 1

infinite as there are infinite numbers between 1000 ^2 and 1001^2

Answer 2

Answer:

The number of non-square numbers between $1000^2$ and $1001^2$ are 2000.

To find:

The non-square numbers between  $1000^2$ and $1001^2$

Solution:

The no. of non-square numbers between  $1000^2$ and $1001^2$ can be found out by finding the difference of $1001^2$ and  $1000^2$

$\begin{array} { c } { \quad = 1001 ^ { 2 } - \left. 1000 ^ { 2 } \right} } \\\\ { = ( 1001 ) ^ { 2 } - ( 1000 ) ^ { 2 } } \\\\ { = ( 1001 + 1000 ) ( 1001 - 1000 ) } \\\\ { = 2001 \times 1 } \\\\ { = 2001 } \end{array}$

Since, 2001 includes either of $1001^2$ or $1000^2$,  

∴ No. of non-square numbers between $1000^2$ and $1001^2$  

= 2001 - 1 = 2000

Therefore, 2000 non-square numbers are there in between $1000^2$ and $1001^2$