What 2 square numbers subtract to make 509?

What two square numbers subtract to make 509? In other words, when you subtract one square number from another square number, the answer is 509. 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 = 509

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

255² - 254² = 509

255² is 65025 and 254² is 64516, therefore the answer to the question "What 2 square numbers subtract to make 509?" is 65025 and 64516 as illustrated below:

65025 - 64516 = 509

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 509. Below we list alternate solutions if available.

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