3) \( \frac{\sqrt{-3}}{\sqrt{48}} \)

To simplify the expression: \[ \frac{\sqrt{-3}}{\sqrt{48}} \] Follow these steps: 1. **Simplify the denominator \(\sqrt{48}\):** \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \] 2. **Simplify the numerator \(\sqrt{-3}\):** Since the square root of a negative number involves the imaginary unit \(i\), we have: \[ \sqrt{-3} = i\sqrt{3} \] 3. **Substitute the simplified forms back into the original expression:** \[ \frac{\sqrt{-3}}{\sqrt{48}} = \frac{i\sqrt{3}}{4\sqrt{3}} \] 4. **Cancel out \(\sqrt{3}\) from the numerator and the denominator:** \[ \frac{i\sqrt{3}}{4\sqrt{3}} = \frac{i}{4} \] **Final Answer:** \[ \frac{i}{4} \]