# Question #7f781

##### 1 Answer
Nov 16, 2014

This is just pure coincidence that

$2 + 2 = 2 \cdot 2 = {2}^{2}$

4 is a perfect square number, meaning that if you multiply a number (let's say $a$) by itself, then you will get $a \cdot a$ or ${a}^{2}$.

$3 \cdot 3 = 9$

That means 9 is a perfect square. But 6 is not.

Refer to square roots. They are basically a reversal to an $a \cdot a$ operation:

$\sqrt{{a}^{2}} = a$

If 9 is square rooted:

$\sqrt{9} = 3$

and if 4 is square rooted:

$\sqrt{4} = 2$.

BUT if 6 is under a square root:

$\sqrt{6} \approx 2.44948974278 \ldots$

You don't get a pretty, round integer perfect squares have to offer.

It is just a mathematical "miracle" that $2 + 2$ and $2 \cdot 2$ equals 4. $3 + 3$ equals 6 and $3 \cdot 3$ (which is just $3 + 3 + 3$) equals 9, so 3s aren't as graceful as numbers.

I mean, there are triangles ... but I digress.