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.