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

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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!

Mathhemathh  Jul 26, 2017
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Look again at your second and third lines of "proof":

$$(2^{\sqrt2})^2 \ne 2^2\\ \text{ }\\ (2^{\sqrt2})^2 = 2^{2\sqrt2}$$

.

Alan  Jul 26, 2017
edited by Alan  Jul 26, 2017
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Thank you.

Mathhemathh  Jul 26, 2017

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