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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?

Rationals Between...

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

Consecutive Squares

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

Root to Poly

Age 14 to 16 Challenge Level:
Find the polynomial $p(x)$ with integer coefficients such that one solution of the equation $p(x)=0$ is $1+\sqrt{2}+\sqrt{3}$.