Simplifying radicals refers to the process of rewriting a radical expression (such as square roots, cube roots, etc.) in its simplest form. The goal is to ensure there are no perfect square (or cube, etc.) factors left inside the radical symbol. Here's the basic process:

### Steps to Simplify a Square Root:
1. **Factor the number inside the radical** into its prime factors.
2. **Look for pairs of prime factors** (for square roots) or groups (for cube roots, etc.).
3. **Move each pair/group outside the radical** (since \(\sqrt{a^2} = a\)).
4. **Multiply the factors outside** and keep the remaining factors inside.

### Example: Simplifying \(\sqrt{72}\)
1. **Factor 72**: \( 72 = 2^3 \times 3^2 \)
2. Look for pairs: \( \sqrt{72} = \sqrt{(2^2 \times 3^2) \times 2} \)
3. Move pairs outside: \( \sqrt{72} = 2 \times 3 \times \sqrt{2} \)
4. Simplify: \( \sqrt{72} = 6\sqrt{2} \)

### Common Rules for Simplifying Radicals:
- \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)
- \(\sqrt{a^2} = a\) for non-negative \(a\)
  
This same method works for cube roots, fourth roots, etc., but instead of looking for pairs, you look for triples (for cube roots), quadruples (for fourth roots), and so on.

Do you want details or have any questions?

Here are 5 questions you might want to explore next:
1. How do you simplify cube roots?
2. Can you simplify \(\sqrt{128}\)?
3. What are the rules for multiplying and dividing radicals?
4. How do you rationalize the denominator in a radical expression?
5. How do you simplify expressions with variables under the radical?

**Tip:** Always check if the number inside the radical has a perfect square (like 4, 9, 16, etc.) as a factor—it makes simplifying faster!

Discover how to simplify radical expressions such as square roots using prime factorization. This detailed guide walks you through the steps, from breaking down numbers into prime factors to simplifying expressions like \(\sqrt{72} = 6\sqrt{2}\). Perfect for students in Grades 8-10.

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