9) \( \sqrt{128 x^{6}}+\sqrt{98 x} 6 \)

Let's simplify the expression: \[ \sqrt{128 x^{6}} + 6 \sqrt{98 x} \] ### Step 1: Simplify \(\sqrt{128 x^{6}}\) 1. **Factor 128:** \(128 = 64 \times 2\) \(\sqrt{64} = 8\) 2. **Simplify \(x^{6}\):** \(\sqrt{x^6} = x^{3}\) because \(\sqrt{x^6} = (x^6)^{1/2} = x^{3}\) 3. **Combine the factors:** \[ \sqrt{128 x^{6}} = \sqrt{64 \times 2 \times x^6} = \sqrt{64} \times \sqrt{2} \times \sqrt{x^6} = 8 \times \sqrt{2} \times x^3 = 8x^3 \sqrt{2} \] ### Step 2: Simplify \(6 \sqrt{98 x}\) 1. **Factor 98:** \(98 = 49 \times 2\) \(\sqrt{49} = 7\) 2. **Simplify the square root:** \[ \sqrt{98 x} = \sqrt{49 \times 2 \times x} = \sqrt{49} \times \sqrt{2x} = 7 \sqrt{2x} \] 3. **Multiply by 6:** \[ 6 \sqrt{98 x} = 6 \times 7 \sqrt{2x} = 42 \sqrt{2x} \] ### Step 3: Combine the Simplified Terms \[ \sqrt{128 x^{6}} + 6 \sqrt{98 x} = 8x^3 \sqrt{2} + 42 \sqrt{2x} \] ### Final Answer \[ 8x^3 \sqrt{2} + 42\, \sqrt{\,2x\,} \]