\begin{tabular}{ll}\hline 3. Simplify the surd: $$ \sqrt{200} $$ & Answer:_] \ \hline 4. Evaluate: $$ \sqrt[8]{63^{8}} $$ & \ & \ & Answer: \ \hline\end{tabular}

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**3. Simplify the surd: $$ \sqrt{200} $$**

1. Express $$200$$ as a product of a perfect square and another factor:
   $$
   200 = 100 \times 2
   $$
   
2. Use the property of square roots $$\sqrt{ab} = \sqrt{a}\sqrt{b}$$:
   $$
   \sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2}
   $$
   
3. Evaluate the square root of the perfect square:
   $$
   \sqrt{100} = 10
   $$
   
4. Write the final simplified form:
   $$
   \sqrt{200} = 10\sqrt{2}
   $$

---

**4. Evaluate: $$ \sqrt[8]{63^{8}} $$**

1. Write the radical expression as an exponent:
   $$
   \sqrt[8]{63^{8}} = (63^{8})^{\frac{1}{8}}
   $$
   
2. Multiply the exponents:
   $$
   (63^{8})^{\frac{1}{8}} = 63^{8 \times \frac{1}{8}} = 63^{1}
   $$
   
3. Conclude the evaluation:
   $$
   \sqrt[8]{63^{8}} = 63
   $$
**3. Simplify the surd: $$ \sqrt{200} $$** $$ \sqrt{200} = 10\sqrt{2} $$ **4. Evaluate: $$ \sqrt[8]{63^{8}} $$** $$ \sqrt[8]{63^{8}} = 63 $$

\begin{tabular}{ll}\hline 3. Simplify the surd: \( \sqrt{200} \) & Answer:_] \\ \hline 4. Evaluate: \( \sqrt[8]{63^{8}} \) & \\ & \\ & Answer: \\ \hline\end{tabular}

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