Factor $48=4^{2}\times 3$. Rewrite the square root of the product $\sqrt{4^{2}\times 3}$ as the product of square roots $\sqrt{4^{2}}\sqrt{3}$. Take the square root of $4^{2}$.
$$A=-3\times 4\sqrt{3}+\sqrt{27}-5\sqrt{147}$$
Multiply $-3$ and $4$ to get $-12$.
$$A=-12\sqrt{3}+\sqrt{27}-5\sqrt{147}$$
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 $3^{2}$.
$$A=-12\sqrt{3}+3\sqrt{3}-5\sqrt{147}$$
Combine $-12\sqrt{3}$ and $3\sqrt{3}$ to get $-9\sqrt{3}$.
$$A=-9\sqrt{3}-5\sqrt{147}$$
Factor $147=7^{2}\times 3$. Rewrite the square root of the product $\sqrt{7^{2}\times 3}$ as the product of square roots $\sqrt{7^{2}}\sqrt{3}$. Take the square root of $7^{2}$.
$$A=-9\sqrt{3}-5\times 7\sqrt{3}$$
Multiply $-5$ and $7$ to get $-35$.
$$A=-9\sqrt{3}-35\sqrt{3}$$
Combine $-9\sqrt{3}$ and $-35\sqrt{3}$ to get $-44\sqrt{3}$.
