### 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?