Radical Dude!
Algebra
Level
5
\[\large \sqrt[8]{527 - \dfrac{1}{527 - \frac{1}{527 - \cdots}}} = \dfrac{\sqrt{a} + \sqrt{b}}{c} , \]
where \(a,b,c\) are positive, square-free integers. Find the product \(abc\).
Details and Assumptions:
- To clarify, it is the \(8^\text{th} \) root that is being taken.
by
Brian Charlesworth