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sqrt5(2sqrt(6x)-sqrt(96 x))

5(26x−96x)\sqrt{5}(2\sqrt{6x}-\sqrt{96x})

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Full solution

Q. 5(26x−96x)\sqrt{5}(2\sqrt{6x}-\sqrt{96x})
  1. Simplify Inside Fifth Root: Simplify the expression inside the fifth root.\newlineCalculation: 96x=96⋅x=4⋅6x\sqrt{96x} = \sqrt{96}\cdot\sqrt{x} = 4\cdot\sqrt{6x}\newlineReasoning: Simplify 96\sqrt{96} as 4⋅64\cdot\sqrt{6}.
  2. Substitute Simplified Expression: Substitute the simplified expression back into the original equation.\newlineCalculation: 26x−46x=−26x2\sqrt{6x} - 4\sqrt{6x} = -2\sqrt{6x}\newlineReasoning: Combine like terms.
  3. Apply Fifth Root: Apply the fifth root to the simplified expression.\newlineCalculation: −26x5\sqrt[5]{-2\sqrt{6x}}\newlineReasoning: Apply the fifth root to the entire expression.

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