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Rationals Between

What fractions can you find between the square roots of 56 and 58?

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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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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?

Smith and Jones

Stage: 4 Challenge Level: Challenge Level:1

Have you listed the square and cube numbers between 13 and 1300?

Consider how many numbers satisfy each set of conditions:
Less than 500, square and cube
Less than 500, square and not cube
Less than 500, not square and cube?