To simplify the expression \( 4\sqrt{8} + 3\sqrt{18} \), follow these steps:

1. **Simplify the square roots:**
   - \( \sqrt{8} \) can be simplified as:
     \[
     \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
     \]
   - \( \sqrt{18} \) can be simplified as:
     \[
     \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
     \]

2. **Substitute the simplified square roots back into the expression:**
   \[
   4\sqrt{8} + 3\sqrt{18} = 4(2\sqrt{2}) + 3(3\sqrt{2})
   \]

3. **Simplify by multiplying the constants:**
   \[
   4(2\sqrt{2}) + 3(3\sqrt{2}) = 8\sqrt{2} + 9\sqrt{2}
   \]

4. **Combine like terms (since both terms have \( \sqrt{2} \) as a common factor):**
   \[
   8\sqrt{2} + 9\sqrt{2} = (8 + 9)\sqrt{2} = 17\sqrt{2}
   \]

So, the simplified expression is \( 17\sqrt{2} \).

Would you like more details or have any questions? Here are five related questions to expand on this topic:

1. How do you simplify \( \sqrt{50} + \sqrt{75} \)?
2. What are the steps to simplify \( 5\sqrt{12} - 2\sqrt{27} \)?
3. Can you multiply \( 3\sqrt{5} \times 2\sqrt{3} \)?
4. How do you add radical expressions with different radicands?
5. What is the process for rationalizing the denominator in a fraction with a square root?

**Tip:** When simplifying square roots, always check if the radicand can be factored into a perfect square and another factor to simplify further.

Learn how to simplify the expression 4√8 + 3√18 step-by-step with detailed explanations and examples. This problem involves simplifying square roots and combining like terms. Suitable for high school students.

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