The expression "radical 189" refers to the square root of 189, denoted as \( \sqrt{189} \).

Let's simplify it step by step:

1. **Prime factorization of 189**:
   \[
   189 = 3^3 \times 7
   \]

2. **Square root**:
   \[
   \sqrt{189} = \sqrt{3^3 \times 7} = \sqrt{3^2 \times 3 \times 7} = 3\sqrt{21}
   \]

Thus, the simplified form of \( \sqrt{189} \) is:
\[
\boxed{3\sqrt{21}}
\]

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. How do you simplify \( \sqrt{72} \)?
2. What is the square root of a number without simplifying?
3. Can you express \( \sqrt{21} \) in decimal form?
4. How would you simplify cube roots, such as \( \sqrt[3]{189} \)?
5. What are the properties of square roots and radical expressions?

**Tip**: Always check if a number has a perfect square factor when simplifying square roots!

Learn how to simplify the square root of 189 using prime factorization. This problem covers key concepts like radicals, square roots, and properties of prime factorization. Perfect for students in Grades 8-10.

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