Proof that 2 <msqrt>

Proof that $2\sqrt{2}+\sqrt{7}$ is an irrational number.
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Giovani Hickman
From
$2\sqrt{2}+\sqrt{7}=\frac{n}{m}$
and
$2\sqrt{2}-\sqrt{7}=\frac{m}{n},$
$4\sqrt{2}=\frac{m}{n}+\frac{n}{m}.$
That is, $\sqrt{2}$ should be rational.