document.write( "Question 1045159: What is the difference between the smallest perfect square larger than 1 million and the largest perfect square smaller than 1 million? \n" ); document.write( "

Algebra.Com's Answer #660539 by Boreal(15235) $\"\"$ $\"About$

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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.
\n" ); document.write( "While we are at it, let's look at the differences in perfect squares
\n" ); document.write( "1,4,9,16,25,36,49,64,81,100.
\n" ); document.write( "The difference between 81 and 100, for example, is 19, which is double +1 the square root of 81
\n" ); document.write( "Therefore, the difference between the perfect square <1 million and the next one is 2x+1.
\n" ); document.write( "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.
\n" ); document.write( "The difference between that square and a million is twice 999+1=1999.
\n" ); document.write( "The next square root is a million, and the difference between that square and the next one is 2001, twice 1000 plus 1.
\n" ); document.write( "Indeed, 1001^2=1002001.
\n" ); document.write( "Therefore, the difference is the sum of 1999 and 2001, or 4000.\r
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