What 2 square numbers subtract to make 685?

What two square numbers subtract to make 685? In other words, when you subtract one square number from another square number, the answer is 685. 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 = 685

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

71² - 66² = 685

71² is 5041 and 66² is 4356, therefore the answer to the question "What 2 square numbers subtract to make 685?" is 5041 and 4356 as illustrated below:

5041 - 4356 = 685

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 685. Below we list alternate solutions if available.

117649 - 116964 = 685

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