Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{i}{4}
\]
Solution
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:**
\[
\frac{i}{4}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
Let's simplify \( \frac{\sqrt{-3}}{\sqrt{48}} \). First, we notice that \( \sqrt{-3} \) can be expressed as \( i\sqrt{3} \), where \( i \) is the imaginary unit. Now, simplifying \( \sqrt{48} \): \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}. \] Now substitute back into the expression: \[ \frac{i\sqrt{3}}{4\sqrt{3}}. \] Since \( \sqrt{3} \) in the numerator and denominator cancels out, we get: \[ \frac{i}{4}. \] So, the simplified form of \( \frac{\sqrt{-3}}{\sqrt{48}} \) is \( \frac{i}{4} \).
