



 
Hi, Have you seen a proof that $\sqrt{2}$ is irrational? There is one in our response to an earlier question. I would use the same technique here. Suppose that $\sqrt{2}+ \sqrt{2} = 2 \sqrt{2}$ is rational then there are integers $p$ and $q$ so that \[2 \sqrt{2} = \frac{p}{q}.\] Square both sides to get \[8 = \frac{p^2}{q^2}\] or \[8 q^2 = p^{2}.\] Can you see how to complete the proof? Write back if you need more assistance. Penny  


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