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Mathematics

Find cube root of −125343\dfrac{-125}{343}

Cube & Cube Roots

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Answer

Prime factors of 125:

Find cube root of -125/343. Cubes and Cube Roots, Concise Mathematics Solutions ICSE Class 8.

Prime factors of 343:

Find cube root of -125/343. Cubes and Cube Roots, Concise Mathematics Solutions ICSE Class 8.

−1253433=−12533433=−(5×5×5)3(7×7×7)3=−57\sqrt[3]{\dfrac{-125}{343}}\\[1em] = {\dfrac{\sqrt[3]{-125}}{\sqrt[3]{343}}}\\[1em] = {-\dfrac{\sqrt[3]{(5 \times 5 \times 5)}}{\sqrt[3]{(7 \times 7 \times 7)}}}\\[1em] = -\dfrac{5}{7}

Hence, −1253433=−57\sqrt[3]{\dfrac{-125}{343}} = {-\dfrac{5}{7}}

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