What 2 square numbers subtract to make 83?

What two square numbers subtract to make 83? In other words, when you subtract one square number from another square number, the answer is 83. 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 = 83

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

42² - 41² = 83

42² is 1764 and 41² is 1681, therefore the answer to the question "What 2 square numbers subtract to make 83?" is 1764 and 1681 as illustrated below:

1764 - 1681 = 83

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 83. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 84?
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