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Be Reasonable

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

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The Root Cause

Prove that if a is a natural number and the square root of a is rational, then it is a square number (an integer n^2 for some integer n.)

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Good Approximations

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

Road Maker 2

Age 16 to 18 Short Challenge Level:

You might like to consider working out the destinations of these paths. It is helpful to move along each path one tile at a time and record the coordinates of one of the vertices as you go.