What 2 square numbers subtract to make 137?

What two square numbers subtract to make 137? In other words, when you subtract one square number from another square number, the answer is 137. 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 = 137

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

69² - 68² = 137

69² is 4761 and 68² is 4624, therefore the answer to the question "What 2 square numbers subtract to make 137?" is 4761 and 4624 as illustrated below:

4761 - 4624 = 137

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 137. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 138?
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