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This question already has an answer here:

Consider the following number:

$$ \sqrt{10} - \sqrt 6 -\sqrt 5 + \sqrt 3 $$

How can I prove that this number is irrational?

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merged by Daniel Fischer Feb 14 '16 at 10:57

This question was merged with Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational because it is an exact duplicate of that question.

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