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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 $1+\sqrt 2+\sqrt 3$.

Surds

Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay

Consecutive Squares

Age 14 to 16 Challenge Level:
What do the eight terms total?
What does this tell you about each side of the equality?