SOLUTION: 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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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?
Answer by MathLover1(20850) About Me  (Show Source):
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it is a number 25 which is a square number of 5, and the sum of+9 and 16 is 25
9 and 16 are also square numbers of 3 and 4
so, 3%5E2%2B4%5E2=5%5E2 or 9%2B16=25
-two square numbers numbers whose sum is 100
number 100 could be written as a sum of 36 and 64
both of these numbers could be written as a square numbers 6%5E2 and 8%5E2
so, 6%5E2%2B8%5E2+=+100+

sqrt%28100%29+=+10; sqrt%281000%29=+31.6, so largest square less than 1000+is 31%5E2
Between 100 and 1000 there are 31-10+=+21 square numbers (22 if 100 itself is included since 100 = 102)