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 Question from Haya: how can i prove the the square root of 2 plus the square root of 2 is an irrational number?

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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