To simplify the radical expression \(\sqrt{32}\), we look for the largest perfect square factor of 32. Here’s how it can be done:

1. **Factor 32 into prime factors:**
   \[
   32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5
   \]

2. **Identify the largest perfect square factor:**
   The largest perfect square factor of \(32\) is \(16\), since \(16 = 4^2\).

3. **Rewrite the square root:**
   \[
   \sqrt{32} = \sqrt{16 \times 2}
   \]

4. **Apply the square root to each factor:**
   \[
   \sqrt{32} = \sqrt{16} \times \sqrt{2}
   \]

5. **Simplify:**
   \[
   \sqrt{16} = 4, \quad \text{so} \quad \sqrt{32} = 4\sqrt{2}
   \]

Thus, the simplified form of \(\sqrt{32}\) is **\(4\sqrt{2}\)**.

Would you like more details on any part of this process, or do you have any questions?

Here are 5 related questions to explore further:

1. How do you simplify \(\sqrt{50}\)?
2. What are the steps to simplify a cube root, such as \(\sqrt[3]{54}\)?
3. How do you rationalize the denominator of \(\frac{1}{\sqrt{5}}\)?
4. What is the simplified form of \(\sqrt{72}\)?
5. How can you simplify \(\sqrt{18} + \sqrt{8}\)?

**Tip:** When simplifying square roots, look for the largest perfect square factor of the number under the square root.

Learn how to simplify the square root of 32 using prime factorization and properties of square roots. This guide provides a detailed, step-by-step solution, perfect for students in Grades 7-9. Understand how to identify perfect square factors and simplify radical expressions.

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