Factor $27=3^{2}\times 3$. Rewrite the square root of the product $\sqrt{3^{2}\times 3}$ as the product of square roots $\sqrt{3^{2}}\sqrt{3}$. Take the square root of $3^{2}$.
$$4\sqrt{3}-30-8\times 3\sqrt{3}+\sqrt{20}$$
Multiply $-8$ and $3$ to get $-24$.
$$4\sqrt{3}-30-24\sqrt{3}+\sqrt{20}$$
Combine $4\sqrt{3}$ and $-24\sqrt{3}$ to get $-20\sqrt{3}$.
$$-20\sqrt{3}-30+\sqrt{20}$$
Factor $20=2^{2}\times 5$. Rewrite the square root of the product $\sqrt{2^{2}\times 5}$ as the product of square roots $\sqrt{2^{2}}\sqrt{5}$. Take the square root of $2^{2}$.
