What 2 square numbers subtract to make 5065?

What two square numbers subtract to make 5065? In other words, when you subtract one square number from another square number, the answer is 5065. 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 = 5065

We solved the equation above and found this to be true:

509² - 504² = 5065

509² is 259081 and 504² is 254016, therefore the answer to the question "What 2 square numbers subtract to make 5065?" is 259081 and 254016 as illustrated below:

259081 - 254016 = 5065

Note that there may be more than one solution to a problem like this. Above, we found the lowest combination of square numbers that subtract to 5065. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 5066?
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