Solution of the Week #431 - Simplify

sqrt(sqrt(80)+sqrt(81))

= sqrt(4*sqrt(5) + 9)

= sqrt(4 + 4*sqrt(5) + 5)

= sqrt(2^2 + 2*2*sqrt(5) + sqrt(5)^2)

= sqrt(2 + sqrt(5))^2

= 2 + sqrt(5)