What 2 square numbers subtract to make 821?

What two square numbers subtract to make 821? In other words, when you subtract one square number from another square number, the answer is 821. 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 = 821

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

411² - 410² = 821

411² is 168921 and 410² is 168100, therefore the answer to the question "What 2 square numbers subtract to make 821?" is 168921 and 168100 as illustrated below:

168921 - 168100 = 821

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 821. Below we list alternate solutions if available.

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