What 2 square numbers subtract to make 4195?

What two square numbers subtract to make 4195? In other words, when you subtract one square number from another square number, the answer is 4195. 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 = 4195

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

422² - 417² = 4195

422² is 178084 and 417² is 173889, therefore the answer to the question "What 2 square numbers subtract to make 4195?" is 178084 and 173889 as illustrated below:

178084 - 173889 = 4195

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 4195. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 4196?
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