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

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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 $100$)


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


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