### Rationals Between...

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

### 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?

# Roots Near 9

##### Age 14 to 16 Short Challenge Level:

Answer: $35$ numbers

$\sqrt n$ is less than $1$ from $9$
$\sqrt n$ is between $8$ and $10$
$n$ is between $64$ and $100$ (but not $64$ or $100$)

$65,66,67,68,...,99$

$\underbrace{\underbrace{1, 2, 3, ..., 64}_{\text{64 numbers}}, 65, 66, 67, 68, ..., 99}_{\text{99 numbers}}$

$99-64=35$

You can find more short problems, arranged by curriculum topic, in our short problems collection.