Question
Simplify. Assume \( j \) is greater than or equal to zero. \( \sqrt{12 j^{6}} \)
Ask by Simpson Ingram. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2 j^{3} \sqrt{3} \)
Solution
To simplify \( \sqrt{12 j^{6}} \) given that \( j \geq 0 \), follow these steps:
1. **Separate the Square Root:**
\[
\sqrt{12 j^{6}} = \sqrt{12} \times \sqrt{j^{6}}
\]
2. **Simplify \( \sqrt{j^{6}} \):**
\[
\sqrt{j^{6}} = j^{3} \quad \text{(since \( j \geq 0 \))}
\]
3. **Simplify \( \sqrt{12} \):**
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]
4. **Combine the Results:**
\[
\sqrt{12 j^{6}} = 2\sqrt{3} \times j^{3} = 2 j^{3} \sqrt{3}
\]
**Final Simplified Form:**
\[
2 j^{3} \sqrt{3}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify \( \sqrt{12 j^{6}} \), we can break it down into parts. Start with the number inside the square root: \( 12 \) can be factored into \( 4 \times 3 \). The square root of \( 4 \) is \( 2 \), so \( \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \). Next, we simplify \( \sqrt{j^6} \). Since the square root of \( j^6 \) is \( j^{6/2} = j^3 \), we can now combine our results. Putting it all together, we have: \[ \sqrt{12 j^{6}} = \sqrt{12} \cdot \sqrt{j^{6}} = 2\sqrt{3} \cdot j^3 = 2j^3\sqrt{3} \] Therefore, the simplified expression is \( 2j^3\sqrt{3} \).
