Question 1045159: What is the difference between the smallest perfect square larger than 1 million and the largest perfect square smaller than 1 million?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Let x be the largest perfect square under one million and (x+2) be the next one, because the square root of a million is 1000.. (x+2)^2 will be the smallest perfect square greater than 1 million.
While we are at it, let's look at the differences in perfect squares
1,4,9,16,25,36,49,64,81,100.
The difference between 81 and 100, for example, is 19, which is double +1 the square root of 81
Therefore, the difference between the perfect square <1 million and the next one is 2x+1.
The square root of a million is 1000. That means 999^2=998001 is the largest number whose square root is less than a million.
The difference between that square and a million is twice 999+1=1999.
The next square root is a million, and the difference between that square and the next one is 2001, twice 1000 plus 1.
Indeed, 1001^2=1002001.
Therefore, the difference is the sum of 1999 and 2001, or 4000.
Answer by ikleyn(52776)  (Show Source):
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