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.
The best solution was submitted by Yang, Hae Hun (양해훈), 2008학번. Congratulations!
Here is his Solution of Problem 2008-11.