What 2 square numbers subtract to make 311?

What two square numbers subtract to make 311? In other words, when you subtract one square number from another square number, the answer is 311. 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 = 311

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

156² - 155² = 311

156² is 24336 and 155² is 24025, therefore the answer to the question "What 2 square numbers subtract to make 311?" is 24336 and 24025 as illustrated below:

24336 - 24025 = 311

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 311. Below we list alternate solutions if available.

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