Simplify. \( 5 \sqrt{18}-\sqrt{162}+8 \sqrt{128} \)

To simplify \( 5 \sqrt{18} - \sqrt{162} + 8 \sqrt{128} \), we'll first simplify each square root. 1. \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \). Therefore, \( 5 \sqrt{18} = 5 \times 3\sqrt{2} = 15\sqrt{2} \). 2. \( \sqrt{162} = \sqrt{81 \times 2} = 9\sqrt{2} \). So, \( -\sqrt{162} = -9\sqrt{2} \). 3. \( \sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2} \). Consequently, \( 8 \sqrt{128} = 8 \times 8\sqrt{2} = 64\sqrt{2} \). Now, put it all together: \[ 15\sqrt{2} - 9\sqrt{2} + 64\sqrt{2} = (15 - 9 + 64)\sqrt{2} = 70\sqrt{2}. \] The simplified expression is \( 70\sqrt{2} \).