Proof that 1*1=2 (help! prove it wrong!)

Now we all know that 1 multiplied by 1 is always 1... right? Anyway, here's the proof:

Let \({2}^{\sqrt{2}} = x\)

Squaring both sides... \({({2}^{\sqrt{2}})}^{2} = {x}^{2}\)

...we get \(2^2 = {x}^2\)

Get the square root of both sides and... \(2 = x\)

Substituting x, we get \(2^{\sqrt{2}} = 2\)

Since any number raised to 1 is itself, then \(2^{\sqrt{2}} = 2^1\)

Therefore, we get \(\sqrt{2} = 1\)

Enough? Nooooooo. Squaring both sides... \({\sqrt{2}}^2 = 1^2\)

...we get \(2 = 1^2\)

Expanding exponents, you get \(2 = 1*1\)

There you have it. My math teacher used to say that I would do well in collage because of stuff like this... Anyway, now I ask everyone out there who's good at math: help prove it wrong!