To express \( \sqrt{200} \) in its simplest radical form, follow these steps:

1. **Factor the number under the square root**:
   \[
   200 = 2^3 \times 5^2
   \]
2. **Group the perfect squares**:
   \[
   200 = (2^2 \times 5^2) \times 2
   \]

3. **Take the square root of the perfect squares**:
   \[
   \sqrt{200} = \sqrt{(2^2 \times 5^2) \times 2} = 2 \times 5 \times \sqrt{2} = 10\sqrt{2}
   \]

Thus, the simplest radical form of \( \sqrt{200} \) is:
\[
\boxed{10\sqrt{2}}
\]

Would you like more details on how to simplify radicals or ask any other questions?

Here are 5 related questions:
1. How do you simplify \( \sqrt{72} \) in radical form?
2. Can you simplify \( \sqrt{50} \) using the same method?
3. What are perfect squares and why do they help in simplifying square roots?
4. How can you simplify cube roots, such as \( \sqrt[3]{54} \)?
5. How do you simplify higher degree roots like \( \sqrt[4]{32} \)?

**Tip:** Always look for perfect square factors when simplifying square roots!

Learn how to express the square root of 200 in its simplest radical form with a step-by-step solution. This problem covers factorization and the properties of square roots, making it suitable for students in Grades 6-8.

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