Let's simplify the expression \(\sqrt{8} + 2\sqrt{32} - 5\sqrt{2}\).

1. **Simplify each square root:**
   - \(\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}\)
   - \(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}\)
   - \(\sqrt{2}\) remains as it is.

2. **Substitute the simplified terms into the original expression:**
   \[
   2\sqrt{2} + 2 \times 4\sqrt{2} - 5\sqrt{2}
   \]

3. **Simplify further by performing the multiplications:**
   \[
   2\sqrt{2} + 8\sqrt{2} - 5\sqrt{2}
   \]

4. **Combine like terms:**
   - \(2\sqrt{2} + 8\sqrt{2} - 5\sqrt{2} = (2 + 8 - 5)\sqrt{2} = 5\sqrt{2}\)

So, the simplified expression is \(5\sqrt{2}\).

Would you like to dive into more details, or do you have any questions?

Here are some related questions for practice:

1. Simplify the expression \(3\sqrt{18} + 4\sqrt{50} - \sqrt{8}\).
2. What is the value of \(7\sqrt{2} + 3\sqrt{18} - 2\sqrt{50}\)?
3. Simplify \(4\sqrt{12} - 3\sqrt{27} + 2\sqrt{75}\).
4. Evaluate \(\sqrt{72} + 2\sqrt{32} - 3\sqrt{50}\).
5. Simplify the expression \(6\sqrt{20} - 4\sqrt{45} + 5\sqrt{5}\).

**Tip:** When simplifying square roots, always look for perfect square factors to reduce the expression.

Learn how to simplify the square root expression √8 + 2√32 - 5√2 with a step-by-step solution. This problem involves simplifying square roots by identifying perfect square factors and combining like terms. Suitable for students in Grades 7-9.

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