What 2 square numbers subtract to make 6566?

What two square numbers subtract to make 6566? In other words, when you subtract one square number from another square number, the answer is 6566. What are the two square numbers?

First, note that a square number is what you get when you multiply a number by itself, which means that the square root of a square number will equal a whole number. Thus, this is what we are solving:

A² - B² = 6566

We listed all square numbers up to one million. Then we tried all different combinations of subtracting one square number from another to see if we could get 6566. We could not find two square numbers that subtract to make 6566.

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What 2 square numbers subtract to make 6567?
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