Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Rationals Between...

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

Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

Equal Temperament

Age 14 to 16 Challenge Level:

Equal temperament means $12$ times you scale up to be equivalent to an overall multiple of $2$

You want to go up seven points to go from C to G