What 2 square numbers subtract to make 419?

What two square numbers subtract to make 419? In other words, when you subtract one square number from another square number, the answer is 419. 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 = 419

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

210² - 209² = 419

210² is 44100 and 209² is 43681, therefore the answer to the question "What 2 square numbers subtract to make 419?" is 44100 and 43681 as illustrated below:

44100 - 43681 = 419

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 419. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 420?
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