Why does $(3\sqrt3)^2 = 27$? How does $(3\sqrt3)^2 = 27$?

I've tried to solve this using binomial expansion and using the FOIL method from which I obtain $9 + 3\sqrt3 +3\sqrt3 + 3$.
it has been a while since I've done this kind of thing so it may be something obvious that I can't see.
Recall that $$(ab)^2 = (a)^2 (b)^2$$

Here, $a = 3$ and $b = \sqrt 3$.

$$(3 \sqrt 3)^2 = (3)^2(\sqrt 3)^2 = 9 \cdot 3 = 27.$$
Here is a rule I think ...


$(a\sqrt b)^2 = (\sqrt (a^2.b)^2$
$(3\sqrt 3)^2 = (\sqrt (3^2.3)^2$
$(3\sqrt 3)^2 = (\sqrt (9.3)^2$
$(3\sqrt 3)^2 = (\sqrt (27)^2$
$(3\sqrt 3)^2 $=  27


Henced proved....