What 2 square numbers subtract to make 312?

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What two square numbers subtract to make 312? In other words, when you subtract one square number from another square number, the answer is 312. 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 = 312

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

19² - 7² = 312

19² is 361 and 7² is 49, therefore the answer to the question "What 2 square numbers subtract to make 312?" is 361 and 49 as illustrated below:

361 - 49 = 312

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 312. Below we list alternate solutions if available.

841 - 529 = 312
1681 - 1369 = 312
6241 - 5929 = 312

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