Powers and roots

There are 62 NRICH Mathematical resources connected to Powers and roots
Deep Roots
problem

Deep roots

Age
14 to 16
Challenge level
filled star filled star filled star
Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$
St Ives
article

St ives

As I was going to St Ives, I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven kittens. Kittens, cats, sacks and wives, how many were going to St Ives?