What 2 square numbers subtract to make 2005?

What two square numbers subtract to make 2005? In other words, when you subtract one square number from another square number, the answer is 2005. 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 = 2005

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

203² - 198² = 2005

203² is 41209 and 198² is 39204, therefore the answer to the question "What 2 square numbers subtract to make 2005?" is 41209 and 39204 as illustrated below:

41209 - 39204 = 2005

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 2005. Below we list alternate solutions if available.

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