1. **State the problem:** Simplify and rationalize the expression $$\sqrt{\frac{18}{2}}$$ assuming all variables represent positive numbers. 2. **Recall the property of square roots:** $$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$$ for positive $a$ and $b$. 3. **Apply the property:** $$\sqrt{\frac{18}{2}} = \frac{\sqrt{18}}{\sqrt{2}}$$ 4. **Simplify the square roots:** $$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$$ 5. **Substitute back:** $$\frac{3\sqrt{2}}{\sqrt{2}}$$ 6. **Cancel common factors:** $$\frac{3\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}} = 3$$ 7. **Final answer:** $$3$$