What 2 square numbers subtract to make 513?

What two square numbers subtract to make 513? In other words, when you subtract one square number from another square number, the answer is 513. 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 = 513

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

23² - 4² = 513

23² is 529 and 4² is 16, therefore the answer to the question "What 2 square numbers subtract to make 513?" is 529 and 16 as illustrated below:

529 - 16 = 513

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 513. Below we list alternate solutions if available.

1089 - 576 = 513
7569 - 7056 = 513
66049 - 65536 = 513

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