1. **State the problem:** Multiply $\sqrt{2}$ and $\sqrt{18}$ and simplify the result. 2. **Recall the multiplication rule for square roots:** $$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \times b}$$ This means we can multiply the numbers inside the square roots and then take the square root of the product. 3. **Apply the rule:** $$\sqrt{2} \cdot \sqrt{18} = \sqrt{2 \times 18}$$ 4. **Calculate the product inside the root:** $$2 \times 18 = 36$$ So, $$\sqrt{2} \cdot \sqrt{18} = \sqrt{36}$$ 5. **Simplify the square root:** Since $36$ is a perfect square, $$\sqrt{36} = 6$$ 6. **Final answer:** $$\boxed{6}$$ This means the product of $\sqrt{2}$ and $\sqrt{18}$ simplifies to 6.