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Be Reasonable

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

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Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

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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.

The Root Cause

Age 16 to 18 Challenge Level:
Why do this problem?
It is instructive as an example of proof using the contrapositive of the statement that must be proved.

Possible approach
The class might discuss the proof in pairs before having a class discussion of the proof. It is very short but needs to be carefully argued.

Key question
What if the statement we are trying to prove were not true?

Possible support
Proof Sorter