Factor $32=4^{2}\times 2$. Rewrite the square root of the product $\sqrt{4^{2}\times 2}$ as the product of square roots $\sqrt{4^{2}}\sqrt{2}$. Take the square root of $4^{2}$.
$$4\sqrt{2}-5\sqrt{8}+3\sqrt{12}$$
Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$4\sqrt{2}-5\times 2\sqrt{2}+3\sqrt{12}$$
Multiply $-5$ and $2$ to get $-10$.
$$4\sqrt{2}-10\sqrt{2}+3\sqrt{12}$$
Combine $4\sqrt{2}$ and $-10\sqrt{2}$ to get $-6\sqrt{2}$.
$$-6\sqrt{2}+3\sqrt{12}$$
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 $2^{2}$.
