Let's simplify the expression:

$\sqrt{8} + \sqrt{18}$

Step 1: Simplify each square root term

• For $\sqrt{8}$: $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

• For $\sqrt{18}$: $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$

Step 2: Combine like terms

Now, we can rewrite the expression as: $2\sqrt{2} + 3\sqrt{2}$

Since both terms have the same square root ($\sqrt{2}$), we can combine the coefficients: $(2 + 3)\sqrt{2} = 5\sqrt{2}$

Final Answer:

$\sqrt{8} + \sqrt{18} = 5\sqrt{2}$

Would you like further explanation or have any other questions? Here's a related set of questions for you:

1. How would you simplify $\sqrt{12} + \sqrt{27}$?
2. Can you explain how to simplify square roots involving variables?
3. What happens if you add different square roots, such as $\sqrt{2}$ and $\sqrt{3}$?
4. What are some methods to simplify expressions with cube roots?
5. How do you handle square roots of negative numbers?

Tip: When simplifying square roots, always look for perfect square factors (like 4, 9, 16, etc.) to break down the expression into simpler components.