\begin{tabular}{l} Add or subtract the radical expressions as indicated. \\ \( 6 \sqrt{48}+3 \sqrt{8}-\sqrt{75}=\square \) \\ \hline\end{tabular}

To simplify the expression \( 6 \sqrt{48} + 3 \sqrt{8} - \sqrt{75} \), follow these steps: 1. **Simplify Each Radical:** - **\(\sqrt{48}\):** \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \] - **\(\sqrt{8}\):** \[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \] - **\(\sqrt{75}\):** \[ \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3} \] 2. **Substitute the Simplified Radicals Back into the Expression:** \[ 6 \sqrt{48} + 3 \sqrt{8} - \sqrt{75} = 6(4\sqrt{3}) + 3(2\sqrt{2}) - 5\sqrt{3} \] 3. **Perform the Multiplications:** \[ = 24\sqrt{3} + 6\sqrt{2} - 5\sqrt{3} \] 4. **Combine Like Terms:** \[ = (24\sqrt{3} - 5\sqrt{3}) + 6\sqrt{2} = 19\sqrt{3} + 6\sqrt{2} \] **Final Answer:** \[ 19\sqrt{3} + 6\sqrt{2} \]