What 2 square numbers subtract to make 1688?

What two square numbers subtract to make 1688? In other words, when you subtract one square number from another square number, the answer is 1688. 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 = 1688

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

213² - 209² = 1688

213² is 45369 and 209² is 43681, therefore the answer to the question "What 2 square numbers subtract to make 1688?" is 45369 and 43681 as illustrated below:

45369 - 43681 = 1688

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 1688. Below we list alternate solutions if available.

178929 - 177241 = 1688

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