Rational and irrational numbers

Find the sum of this series of surds.

Can you express every recurring decimal as a fraction?

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

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.

What fractions can you find between the square roots of 65 and 67?

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Can you make a square from these triangles?

Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?