Rational and irrational numbers

problem
The clue is in the question

Age

16 to 18

Challenge level

Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?
problem
Irrational arithmagons

Age

16 to 18

Challenge level

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
problem
Rational round

Age

16 to 18

Challenge level

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
problem
Road maker 2

Age

16 to 18

Challenge level

Can you work out where the blue-and-red brick roads end?