TITLE: finding the difference of perfect squares
QUESTION [5 upvotes]: Find the difference between the smallest perfect square larger than one million and the largest perfect square smaller than one million.

I did not want to use a calculator for this question. I read this in a mathematical teaser book and was not sure how to solve it. I tried doing this with smaller numbers such as $10.$ The smallest perfect square larger than ten would would be $16$ and the smallest perfect square next to ten would be $9.$ I found the difference of those to be $7$ Then I tried this for $100.$ I found that the smallest perfect square is $81$ and the largest perfect square to be $121.$ I found the difference of those to be $40.$ 
However, I cannot seem to solve the one million question. Can someone help me to solve this? I was working on it for sometime now and would like to see how to solve it.

REPLY [5 votes]: We want $(x+1)^2-(x-1)^2$, where $x=1000$. 
The difference is $4x$, that is, $4000$.