What 2 square numbers subtract to make 511?

What two square numbers subtract to make 511? In other words, when you subtract one square number from another square number, the answer is 511. 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 = 511

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

40² - 33² = 511

40² is 1600 and 33² is 1089, therefore the answer to the question "What 2 square numbers subtract to make 511?" is 1600 and 1089 as illustrated below:

1600 - 1089 = 511

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 511. Below we list alternate solutions if available.

65536 - 65025 = 511

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