Are They Rational?
Number Theory
Level
2
There exist three distinct rational numbers \(a\), \(b\), and \(c\) such that \(\sqrt{a}+\sqrt{b}+\sqrt{c}\) is also rational. At least how many of \(\sqrt{a}\), \(\sqrt{b}\), and \(\sqrt{c}\) have to be rational?
by
Lemuel Liverosk