\begin{tabular}{l} 2. Evaluate: \( \sqrt[3]{8^{2}}= \) \\ \hline Simplify the surd: \( \sqrt{200} \) \\ Answer: \\ \hline Evaluate: \( \sqrt[8]{63^{8}} \) \\ Answer: \\ \hline\end{tabular}

1. Evaluate \( \sqrt[3]{8^{2}} \) - Express \(8\) as a power of 2: \(8 = 2^3\). - Then, \(8^2 = (2^3)^2 = 2^{6}\). - Now, take the cube root: \[ \sqrt[3]{2^{6}} = 2^{\frac{6}{3}} = 2^{2} = 4. \] 2. Simplify the surd \( \sqrt{200} \) - Factorize 200 as \(200 = 100 \times 2\). - Then, \[ \sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \cdot \sqrt{2} = 10\sqrt{2}. \] 3. Evaluate \( \sqrt[8]{63^{8}} \) - Recognize that \(\sqrt[8]{63^{8}}\) represents the eighth root of \(63^{8}\), which gives back the original number (since \(63\) is positive): \[ \sqrt[8]{63^{8}} = 63. \]