+0  
 
+1
80
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avatar+214 

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!

 

 

 

 

 

cheeky

Mathhemathh  Jul 26, 2017
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2+0 Answers

 #1
avatar+25982 
+3

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
 #2
avatar+214 
+2

Thank you.

Mathhemathh  Jul 26, 2017

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