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

Question

UpStudy AI · Accepted Answer

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:**

$$
\frac{i}{4}
$$
$$ \frac{i}{4} $$

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