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

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Rachel's Problem

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

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?