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To simplify \( \sqrt{54} \), we break it down step by step:

### Step 1: Prime factorization of 54
The number \( 54 \) can be factored into:
\[
54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^3
\]

### Step 2: Apply the square root
The square root of \( 54 \) is:
\[
\sqrt{54} = \sqrt{2 \times 3^3}
\]

We can split the square root as:
\[
\sqrt{54} = \sqrt{2} \times \sqrt{3^3}
\]

### Step 3: Simplify perfect squares
Within \( \sqrt{3^3} \), the \( 3^2 \) part can be simplified:
\[
\sqrt{3^3} = \sqrt{3^2 \times 3} = \sqrt{3^2} \times \sqrt{3} = 3\sqrt{3}
\]

Thus:
\[
\sqrt{54} = \sqrt{2} \times 3\sqrt{3} = 3\sqrt{6}
\]

### Final Answer:
\[
\sqrt{54} = 3\sqrt{6}
\]

Would you like further details or have additional questions?

### Related Questions:
1. What is the process to simplify square roots for larger numbers?
2. Can you explain how to identify perfect squares within a number?
3. What is the difference between simplifying and approximating square roots?
4. How do you handle square roots of decimals?
5. Can this approach be used for cube roots?

**Tip:** Always break numbers into prime factors when simplifying square roots—it reveals perfect squares easily!

Simplify \( \sqrt{54} \). Show all your work.

Learn how to simplify \( \sqrt{54} \) with a step-by-step solution. This guide uses prime factorization and properties of square roots to simplify expressions, perfect for students in Grades 6-8.

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