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?
For making 8, everyone noticed that the only ways of doing this are $2^3$, and $64^\frac{1}{2}$, which is $4^\frac{3}{2}=2^3$, and so these are the same.
Zack, Haren and Niall from JAPS made $125$ by doing $5^3$ where $3=81^\frac{1}{4}$
Tom from Devenport Boys gave an explanation of why the last two values are unobtainable;
$89$ is a prime number, and so its only factors are $1$ and $89$, which also means that all its powers, such as $89^2$, will only have factors $1, 89, 7921$ and so on, so it is not a power of any other numbers, and so cannot be achieved.
$216=6^3$, and there is no way of achieving 6 with the values given, with a similar factor method.