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root(3)(-54)

−543 \sqrt[3]{-54}

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Full solution

Q. −543 \sqrt[3]{-54}
  1. Identify number and root: Identify the number and the root to be calculated. Calculate the cube root of −54-54.
  2. Break down into prime factors: Break down −54-54 into its prime factors.\newline−54=−1×3×3×3×2-54 = -1 \times 3 \times 3 \times 3 \times 2\newline=−1×33×2= -1 \times 3^3 \times 2
  3. Apply cube root to factors: Apply the cube root to each factor.\newline−543=−1×33×23\sqrt[3]{-54} = \sqrt[3]{-1 \times 3^3 \times 2}\newline=−13×333×23= \sqrt[3]{-1} \times \sqrt[3]{3^3} \times \sqrt[3]{2}\newline=−1×3×23= -1 \times 3 \times \sqrt[3]{2}
  4. Simplify the expression: Simplify the expression.\newline−1×3×23=−3×23-1 \times 3 \times \sqrt[3]{2} = -3 \times \sqrt[3]{2}

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