What 2 square numbers subtract to make 9732?

What two square numbers subtract to make 9732? In other words, when you subtract one square number from another square number, the answer is 9732. 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 = 9732

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

814² - 808² = 9732

814² is 662596 and 808² is 652864, therefore the answer to the question "What 2 square numbers subtract to make 9732?" is 662596 and 652864 as illustrated below:

662596 - 652864 = 9732

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 9732. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 9733?
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