To simplify the square root of 54, we follow these steps:

1. **Find the prime factors of 54**:
   - \( 54 = 2 \times 27 \)
   - \( 27 = 3 \times 9 \)
   - \( 9 = 3 \times 3 \)

   So, the prime factorization of 54 is:
   \[
   54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^3
   \]

2. **Pair the factors under the square root**:
   \[
   \sqrt{54} = \sqrt{2 \times 3 \times 3 \times 3}
   \]

3. **Identify and simplify perfect squares**:
   - The factor \( 3 \times 3 = 9 \) is a perfect square.

   Therefore:
   \[
   \sqrt{54} = \sqrt{(3 \times 3) \times (2 \times 3)} = 3\sqrt{6}
   \]

So, the simplified form of \(\sqrt{54}\) is:

\[
\sqrt{54} = 3\sqrt{6}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you find the prime factorization of a number?
2. How do you simplify square roots of non-perfect square numbers?
3. What are perfect squares and how do they help in simplifying square roots?
4. How do you simplify expressions with higher roots, like cube roots?
5. Can you simplify \(\sqrt{72}\) using the same method?

**Tip:** Always look for the largest perfect square factor of the number under the square root to simplify it efficiently.

Learn how to simplify the square root of 54 using prime factorization and recognizing perfect squares. This step-by-step solution is suitable for students in Grades 7-9, covering the key concepts of simplifying radicals and prime factorization.

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