document.write( "Question 490372: What is the smallest square number that is the sum of two square numbers. Find two square numbers numbers whose sum is 100. How many square numbers are there between 100 and 1000?
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Algebra.Com's Answer #334029 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "it is a number $\"25\"$ which is a square number of $\"5\"$ , and the sum of $\"+9\"$ and $\"16\"$ is $\"25\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9\"$ and $\"16\"$ are also square numbers of $\"3\"$ and $\"4\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"3%5E2%2B4%5E2=5%5E2\"$ or $\"9%2B16=25\"$ \r
\n" ); document.write( "\n" ); document.write( "-two square numbers numbers whose sum is $\"100\"$ \r
\n" ); document.write( "\n" ); document.write( "number $\"100\"$ could be written as a sum of $\"36\"$ and $\"64\"$
\n" ); document.write( "both of these numbers could be written as a square numbers $\"6%5E2\"$ and $\"8%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"6%5E2%2B8%5E2+=+100+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28100%29+=+10\"$ ; $\"sqrt%281000%29=+31.6\"$ , so largest square less than $\"1000+\"$ is $\"31%5E2\"$
\n" ); document.write( "Between $\"100\"$ and $\"1000\"$ there are $\"31-10+=+21\"$ square numbers (22 if 100 itself is included since 100 = 102)
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