Today my teacher taught about a method to find the greatest integer less than or equal to $(a+\sqrt{b})^n$, in a method mentioned as in here.
But actually the limitation is that $|{a-\sqrt{b}}|$ must be less than $1$.
My question is how to find the same for $|{a-\sqrt{b}}|>1$ (of course, without using a calculator!), say for $(1+\sqrt{5})^6$.
I don't really have an idea of how to go about it.