Let's simplify the given expression:

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

Step 1: Factor each square root

Break each number inside the square root into its prime factors:

$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$

Step 2: Combine like terms

Since both terms have $\sqrt{2}$, we can add their coefficients:

$2\sqrt{2} + 3\sqrt{2} = (2+3)\sqrt{2} = 5\sqrt{2}$

Final Answer:

$\boxed{5\sqrt{2}}$

Would you like a breakdown of any step?

Here are five related questions to practice:

1. Simplify $\sqrt{12} + \sqrt{27}$.
2. Simplify $\sqrt{50} - \sqrt{8}$.
3. Factor and simplify $\sqrt{32} + \sqrt{18}$.
4. Evaluate $\sqrt{200} + \sqrt{50}$.
5. Express $\sqrt{72} + \sqrt{98}$ in simplest form.

Tip:

Always look for perfect square factors when simplifying square roots!