What 2 square numbers subtract to make 4172?

What two square numbers subtract to make 4172? In other words, when you subtract one square number from another square number, the answer is 4172. 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 = 4172

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

156² - 142² = 4172

156² is 24336 and 142² is 20164, therefore the answer to the question "What 2 square numbers subtract to make 4172?" is 24336 and 20164 as illustrated below:

24336 - 20164 = 4172

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 4172. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 4173?
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