### Ab Surd Ity

Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).

### Absurdity Again

What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?

### Em'power'ed

Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?

# Bina-ring

##### Age 16 to 18Challenge Level

Consider $(1 + \sqrt2)^n$. This will be of the form $A + B\sqrt2$ where $A$ and $B$ are integers. Decide which entries in the table below are possibe and which are not.
 A even A odd B even B odd

What happens for $(a + \sqrt p)^n$ for other values of $p$?