Simplify. \( 6 \sqrt{72}-\sqrt{128}+3 \sqrt{98} \)

To simplify the expression \( 6 \sqrt{72} - \sqrt{128} + 3 \sqrt{98} \), we first break down each square root. 1. For \( \sqrt{72} \): \[ \sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2} \] Thus, \[ 6 \sqrt{72} = 6 \cdot 6\sqrt{2} = 36\sqrt{2} \] 2. For \( \sqrt{128} \): \[ \sqrt{128} = \sqrt{64 \cdot 2} = \sqrt{64} \cdot \sqrt{2} = 8\sqrt{2} \] 3. For \( 3 \sqrt{98} \): \[ \sqrt{98} = \sqrt{49 \cdot 2} = \sqrt{49} \cdot \sqrt{2} = 7\sqrt{2} \] Thus, \[ 3 \sqrt{98} = 3 \cdot 7\sqrt{2} = 21\sqrt{2} \] Now we can substitute these simplified forms back into the original expression: \[ 36\sqrt{2} - 8\sqrt{2} + 21\sqrt{2} \] Next, combine the terms: \[ (36 - 8 + 21)\sqrt{2} = 49\sqrt{2} \] Thus, the simplified expression is: \[ \boxed{49\sqrt{2}} \]