What 2 square numbers subtract to make 823?

What two square numbers subtract to make 823? In other words, when you subtract one square number from another square number, the answer is 823. 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 = 823

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

412² - 411² = 823

412² is 169744 and 411² is 168921, therefore the answer to the question "What 2 square numbers subtract to make 823?" is 169744 and 168921 as illustrated below:

169744 - 168921 = 823

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 823. Below we list alternate solutions if available.

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