What 2 square numbers subtract to make 309?

What two square numbers subtract to make 309? In other words, when you subtract one square number from another square number, the answer is 309. 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 = 309

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

53² - 50² = 309

53² is 2809 and 50² is 2500, therefore the answer to the question "What 2 square numbers subtract to make 309?" is 2809 and 2500 as illustrated below:

2809 - 2500 = 309

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 309. Below we list alternate solutions if available.

24025 - 23716 = 309

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