Analyse and assess the cube root of $11\sqrt{2}+9\sqrt{3}$.

$11\sqrt{2}+9\sqrt{3}$

(a+b)³=a³+b³+3a²b+3ab²

re write $11\sqrt{2}+9\sqrt{3}$ as

$2\sqrt{2}+3\sqrt{3}+9\sqrt{2}+6\sqrt{3}$

$a^3=2\sqrt{2} b^3=3\sqrt{3}$

$3a^{2}b=6\sqrt{3} 3a{b}^2=9\sqrt{2}$

So cube root of $11\sqrt{2}+9\sqrt{3}$  is $\sqrt{2}+\sqrt{3}$