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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?

Rachel's Problem

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

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

Fibonacci sequence. Making and proving conjectures. Creating and manipulating expressions and formulae. Expanding and factorising quadratics. Surds. Powers & roots. Polynomial functions and their roots. Indices. Other equations. Mathematical reasoning & proof.