2008-11 Sum of square roots

Let a, b, c, d be positive rational numbers. Prove that if \(\sqrt a+\sqrt b+\sqrt c+\sqrt d\) is rational, then each of \(\sqrt a\), \(\sqrt b\), \(\sqrt c\), and \(\sqrt d\) is rational.

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2008-11 Sum of square roots, 3.0 out of 5 based on 1 rating