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

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 squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

This problem is taken from the UKMT Mathematical Challenges.