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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?

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Rationals Between...

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

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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