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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?

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

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 $1+\sqrt{2}+\sqrt{3}$.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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