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 $2^{2}$.
Combine $5\sqrt{2}$ and $4\sqrt{2}$ to get $9\sqrt{2}$.
$$9\sqrt{2}-3\sqrt{32}+4\sqrt{128}$$
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 $4^{2}$.
$$9\sqrt{2}-3\times 4\sqrt{2}+4\sqrt{128}$$
Multiply $-3$ and $4$ to get $-12$.
$$9\sqrt{2}-12\sqrt{2}+4\sqrt{128}$$
Combine $9\sqrt{2}$ and $-12\sqrt{2}$ to get $-3\sqrt{2}$.
$$-3\sqrt{2}+4\sqrt{128}$$
Factor $128=8^{2}\times 2$. Rewrite the square root of the product $\sqrt{8^{2}\times 2}$ as the product of square roots $\sqrt{8^{2}}\sqrt{2}$. Take the square root of $8^{2}$.
$$-3\sqrt{2}+4\times 8\sqrt{2}$$
Multiply $4$ and $8$ to get $32$.
$$-3\sqrt{2}+32\sqrt{2}$$
Combine $-3\sqrt{2}$ and $32\sqrt{2}$ to get $29\sqrt{2}$.
