I can simplify the elements but the question does not make any sense.
Α= √(√81) +3√8:√2+8√3:(1+√3)/(3+√3)
\(Α=\sqrt9 +3*2\sqrt2:√2+8√3:\frac{(1+√3)}{(3+√3) }\\ Α=3 +6\sqrt2:\sqrt2+8\sqrt3:\frac{(1+\sqrt3)}{(3+\sqrt3)} \times \frac{(3-\sqrt3) }{(3-\sqrt3) }\\ Α=3 +6\sqrt2:\sqrt2+8\sqrt3:\frac{3-\sqrt3+3\sqrt3-3}{9-3}\\ Α=3 +6\sqrt2:\sqrt2+8\sqrt3:\frac{\sqrt3}{3}\\\)