Rationals Between

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

Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

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:

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?