A past examination paper had the following question that I found interesting. I tried having a go at it but haven't come around with any solutions. How would one go about tackling it?
$$\sqrt {x + \sqrt {4x + \sqrt {16x + \sqrt {64x + 5}}}} - \sqrt x = 1$$
I'm seeing a relation between $4x$, $16x$ and $64x$ so maybe the larger can be simplified to the smaller?
I do encourage you to working within an examination environment (thus not making use of anything other than pen and paper and possibly a calculator).
EDIT: My question had a missing $-\sqrt x$ at the end, sorry!