Let $m,n,p$ be rational numbers such that $\sqrt{m} + \sqrt{n} + \sqrt{p}$ is a rational number. Prove that $\sqrt{m}, \sqrt{n}, \sqrt{p}$ are also rational numbers
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Tags: symmetry
Let $m,n,p$ be rational numbers such that $\sqrt{m} + \sqrt{n} + \sqrt{p}$ is a rational number. Prove that $\sqrt{m}, \sqrt{n}, \sqrt{p}$ are also rational numbers