What 2 square numbers subtract to make 2007?

What two square numbers subtract to make 2007? In other words, when you subtract one square number from another square number, the answer is 2007. 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 = 2007

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

116² - 107² = 2007

116² is 13456 and 107² is 11449, therefore the answer to the question "What 2 square numbers subtract to make 2007?" is 13456 and 11449 as illustrated below:

13456 - 11449 = 2007

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 2007. Below we list alternate solutions if available.

112896 - 110889 = 2007

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