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Why are some numbers called "perfect squares"?


Imagine you have 12 soldiers, and you align them in rows and columns. There are different ways to do this:

1 row of 12 soldiers, or
2 rows of 6 soldiers, or
3 rows of 4 soldiers.

To a bird, 12 soldiers in rows look like a rectangle, like this:


or like this:


or like this:



However, if you have 9 or 16 soldiers, for example, you can form a perfect square, not only a rectangle:


You can do the same with 25, 36, 49,... all those numbers have an exact square root.

And yes, that is why we call that a square root!

Now, can you guess why we call "cube roots" that?

JJCC