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## 'Rational Roots' printed from http://nrich.maths.org/

Suppose that a and b are natural numbers. If $\sqrt{a} + \sqrt{b}$
is rational then show that it is a natural number. Show that,
indeed both $\sqrt{a}$ and $\sqrt{b}$ are then integers.

Suppose that a, b and c are natural numbers. If $\sqrt{a} +
\sqrt{b} + \sqrt{c}$ is rational then show that it is a natural
number. Moreover show that $\sqrt{a}$ , $\sqrt{b}$ and $\sqrt{c}$
are then integers.