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To simplify the expression \(8\sqrt{2} - 4\sqrt{8}\), follow these steps:

1. **Simplify \(\sqrt{8}\)**:
   \[
   \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
   \]

2. **Substitute \(\sqrt{8}\) in the original expression**:
   \[
   8\sqrt{2} - 4\sqrt{8} = 8\sqrt{2} - 4(2\sqrt{2})
   \]

3. **Multiply inside the parentheses**:
   \[
   8\sqrt{2} - 8\sqrt{2}
   \]

4. **Combine like terms**:
   \[
   8\sqrt{2} - 8\sqrt{2} = 0
   \]

The simplified expression is **0**.

Would you like further details on this solution? Here are some related questions to consider:

1. How do you simplify other expressions with square roots like \(\sqrt{18}\)?
2. Can you explain how to factor out the greatest common factor in algebraic expressions?
3. What is the general method to combine like terms involving square roots?
4. How would you approach a similar problem involving cube roots?
5. Why does \(\sqrt{8} = 2\sqrt{2}\)?

**Tip**: When simplifying expressions with square roots, always look for perfect squares that can be factored out to make the square root easier to simplify.

Learn how to simplify the expression 8√2 - 4√8 step-by-step. Understand the process of simplifying square roots and combining like terms in algebraic expressions. Suitable for students in Grades 9-12.

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