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Be Reasonable
Age 16 to 18
Challenge Level 
Prove that there is no arithmetic progression containing all three of $\sqrt{2}$, $\sqrt{3}$ and $\sqrt{5}$.
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Good Approximations
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
Rational Roots
Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
