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 $4^{2}$.
$$4+7\times 4\sqrt{2}-3\sqrt{500}$$
Multiply $7$ and $4$ to get $28$.
$$4+28\sqrt{2}-3\sqrt{500}$$
Factor $500=10^{2}\times 5$. Rewrite the square root of the product $\sqrt{10^{2}\times 5}$ as the product of square roots $\sqrt{10^{2}}\sqrt{5}$. Take the square root of $10^{2}$.
