How do you simplify 2 cubed root 81 + 3 cubed root 24?

##12 root{3}(3)##

Work out the prime factorisations of the numbers under the square roots, this will help simplify, since roots split up;

##2 root{3}(81) + 3 root{3}(24) = 2root{3}(3^{4}} + 3 root{3}(2^{3} cdot 3) = 2root{3}(3 cdot 3^{3}} + 3 root{3}(2^{3}) cdot root{3}(3)## ##= 2 cdot root{3}(3) cdot root{3}(3^{3}) + 3 cdot 2 cdot root{3}(3)## ##=2 cdot 3 cdot root{3}(3) + 6 cdot root{3}(3) = 6 cdot root{3}(3) + 6 cdot root{3}(3) = 12 root{3}(3) ##