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 $4^{2}$.
Combine $4\sqrt{3}$ and $12\sqrt{3}$ to get $16\sqrt{3}$.
$$16\sqrt{3}-\frac{5}{2}\sqrt{12}$$
Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.
$$16\sqrt{3}-\frac{5}{2}\times 2\sqrt{3}$$
Cancel out $2$ and $2$.
$$16\sqrt{3}-5\sqrt{3}$$
Combine $16\sqrt{3}$ and $-5\sqrt{3}$ to get $11\sqrt{3}$.
