Simplify. Assume \( j \) is greater than or equal to zero. \( \sqrt{12 j^{6}} \)

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 \( 2j^3\sqrt{3} \).