What 2 square numbers subtract to make 1001?

What two square numbers subtract to make 1001? In other words, when you subtract one square number from another square number, the answer is 1001. 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 = 1001

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

45² - 32² = 1001

45² is 2025 and 32² is 1024, therefore the answer to the question "What 2 square numbers subtract to make 1001?" is 2025 and 1024 as illustrated below:

2025 - 1024 = 1001

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 1001. Below we list alternate solutions if available.

2601 - 1600 = 1001
5625 - 4624 = 1001
251001 - 250000 = 1001

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