Factor $18=3^{2}\times 2$. Rewrite the square root of the product $\sqrt{3^{2}\times 2}$ as the product of square roots $\sqrt{3^{2}}\sqrt{2}$. Take the square root of $3^{2}$.
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 $2^{2}$.
Factor $200=10^{2}\times 2$. Rewrite the square root of the product $\sqrt{10^{2}\times 2}$ as the product of square roots $\sqrt{10^{2}}\sqrt{2}$. Take the square root of $10^{2}$.
Consider $\left(8-8\sqrt{2}\right)\left(8+8\sqrt{2}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
