What 2 square numbers subtract to make 657?

What two square numbers subtract to make 657? In other words, when you subtract one square number from another square number, the answer is 657. 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 = 657

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

41² - 32² = 657

41² is 1681 and 32² is 1024, therefore the answer to the question "What 2 square numbers subtract to make 657?" is 1681 and 1024 as illustrated below:

1681 - 1024 = 657

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 657. Below we list alternate solutions if available.

12321 - 11664 = 657
108241 - 107584 = 657

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