Simplify. \( -\frac{5}{6} \sqrt{72 p} \)

To simplify \( -\frac{5}{6} \sqrt{72 p} \), we start by simplifying the square root. We know that \( \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \). Therefore, we can rewrite it as: \[ -\frac{5}{6} \sqrt{72 p} = -\frac{5}{6} \sqrt{72} \sqrt{p} = -\frac{5}{6} \times 6 \sqrt{2} \sqrt{p} \] Now multiply \( -\frac{5}{6} \) by 6: \[ -\frac{5}{6} \times 6 = -5 \] Thus, the expression simplifies to: \[ -5 \sqrt{2p} \] So, the final simplified result is: \[ -5 \sqrt{2p} \]