What 2 square numbers subtract to make 7824?

What two square numbers subtract to make 7824? In other words, when you subtract one square number from another square number, the answer is 7824. 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 = 7824

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

175² - 151² = 7824

175² is 30625 and 151² is 22801, therefore the answer to the question "What 2 square numbers subtract to make 7824?" is 30625 and 22801 as illustrated below:

30625 - 22801 = 7824

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 7824. Below we list alternate solutions if available.

110224 - 102400 = 7824
243049 - 235225 = 7824
429025 - 421201 = 7824

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