### Ab Surd Ity

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

### Binomial

By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn

### Proofs with Pictures

Some diagrammatic 'proofs' of algebraic identities and inequalities.

# Particularly General

##### Stage: 5 Challenge Level:

Expand out the brackets in a systematic, organised manner.

You will need to use a double angle trig formula and difference of two squares. Considering $n=1$ might be useful.

There is perhaps no need to provide a proof for your identities if you are very clear in your mind how such a proof would be constructed, although you might wish to produce a proof if interested.