1. **State the problem:** Simplify the expression $$\frac{\sqrt{27}}{\sqrt{12}}$$. 2. **Use the property of square roots:** $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$. 3. Apply this property: $$\frac{\sqrt{27}}{\sqrt{12}} = \sqrt{\frac{27}{12}}$$ 4. Simplify the fraction inside the square root: $$\frac{27}{12} = \frac{\cancel{3} \times 9}{\cancel{3} \times 4} = \frac{9}{4}$$ 5. So the expression becomes: $$\sqrt{\frac{9}{4}}$$ 6. Use the property of square roots for fractions: $$\sqrt{\frac{9}{4}} = \frac{\sqrt{9}}{\sqrt{4}}$$ 7. Calculate the square roots: $$\frac{\sqrt{9}}{\sqrt{4}} = \frac{3}{2}$$ **Final answer:** $$\frac{3}{2}$$