Infinite Nested Radicals
Number Theory
Level
3
\[ \sqrt { 10n\times \sqrt { n\sqrt { n\sqrt { n\ldots } } } \times \sqrt { (n-1)\sqrt { (n-1)\sqrt { (n-1)\ldots } } \times \ldots\times \sqrt { 3\sqrt { 3\sqrt { 3\ldots} } } } } =60n\]
What is the value of \(n\)?
This problem is inspired by Adam Pet's Infinite factorials problem
by
Abyoso Hapsoro