What fractions can you find between the square roots of 65 and 67?

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?

Find integer solutions to: $${{\sqrt{a + b\sqrt{x}}} + {\sqrt{c + d\sqrt{x}}}} ={ 1}$$

Hint: As everything on the left is positive and the total is 1, there are only a few cases to consider.