What 2 square numbers subtract to make 617?

What two square numbers subtract to make 617? In other words, when you subtract one square number from another square number, the answer is 617. 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 = 617

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

309² - 308² = 617

309² is 95481 and 308² is 94864, therefore the answer to the question "What 2 square numbers subtract to make 617?" is 95481 and 94864 as illustrated below:

95481 - 94864 = 617

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 617. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 618?
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