What 2 square numbers subtract to make 9809?

What two square numbers subtract to make 9809? In other words, when you subtract one square number from another square number, the answer is 9809. 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 = 9809

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

297² - 280² = 9809

297² is 88209 and 280² is 78400, therefore the answer to the question "What 2 square numbers subtract to make 9809?" is 88209 and 78400 as illustrated below:

88209 - 78400 = 9809

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 9809. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 9810?
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