What 2 square numbers subtract to make 503?

What two square numbers subtract to make 503? In other words, when you subtract one square number from another square number, the answer is 503. 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 = 503

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

252² - 251² = 503

252² is 63504 and 251² is 63001, therefore the answer to the question "What 2 square numbers subtract to make 503?" is 63504 and 63001 as illustrated below:

63504 - 63001 = 503

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 503. Below we list alternate solutions if available.

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