How can you simplify $\sqrt{9-6\sqrt{2}}$? How do you simplify: $$\sqrt{9-6\sqrt{2}}$$
A classmate of mine changed it to $$\sqrt{9-6\sqrt{2}}=\sqrt{a^2-2ab+b^2}$$ but I'm not sure how that helps or why it helps.
This questions probably too easy to be on the Math Stack Exchange but I'm not sure where else to post it.

Your class mate is being.... clever.
If $\sqrt {9-6\sqrt 2}=a-b $ then $9-6\sqrt 2=a^2-2ab+c^3$
Let $2ab=6\sqrt 2$ and $a^2+b^2=9$.
Can we do that? 
If we let $b^2=k $ and $a^2=9-k$ then $ab=\sqrt {k (9-k)}=3\sqrt 2=\sqrt {18} $.  Solving $k (9-k)=18$ for $k $ (if it isn't visiblely obvious that we can do it in our heads, it is just a quadratic that we can solve by quadratic formula) and, for covenience, choicing the smaller solution (because we want $a>b $), we get $k =3$ is a good solution..
So $a=\sqrt 6$ and $b=\sqrt 3$.
I.e. in other words
$\sqrt {9-6\sqrt 2}=$
$\sqrt {6-2\sqrt 6\sqrt 3 +3}=$
$\sqrt {(\sqrt 6- \sqrt 3)^2}=$
$|\sqrt 6 - \sqrt 3|=$
$\sqrt 6 -\sqrt 3$.
