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Mathematics

Find the cube root of 110.592

Cube & Cube Roots

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Answer

110.5923=11059210003=110592310003\sqrt[3]{110.592}\\[1em] = \sqrt[3]{\dfrac{110592}{1000}}\\[1em] = \dfrac{\sqrt[3]{110592}}{\sqrt[3]{1000}}

Prime factors of 110592:

Find the cube root of 110.592. Cubes and Cube Roots, Concise Mathematics Solutions ICSE Class 8.

∴110592310003=(2×2×2)×(2×2×2)×(2×2×2)×(2×2×2)×(3×3×3)3(10×10×10)3=2×2×2×2×310=4810=4.8\therefore \dfrac{\sqrt[3]{110592}}{\sqrt[3]{1000}} = \dfrac{\sqrt[3]{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times(2 \times 2 \times 2) \times (2 \times 2 \times 2)\times (3 \times 3 \times 3)}}{\sqrt[3]{(10 \times 10 \times 10)}}\\[1em] = \dfrac{{2 \times 2 \times 2 \times 2 \times 3}}{{10}}\\[1em] = \dfrac{{48}}{{10}}\\[1em] = 4.8

Hence, 110.5923=4.8\sqrt[3]{110.592} = 4.8

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