Find the cube-roots of 729−1331\dfrac{729}{-1331}−1331729
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Prime factors of 729:
Prime factors of 1331:
729−13313=−7293−13313=−(3×3×3)×(3×3×3)3(11×11×11)3=−3×311=−911\sqrt[3]{\dfrac{729}{-1331}}\\[1em] = -\dfrac{\sqrt[3]{729}}{\sqrt[3]{-1331}}\\[1em] = -\dfrac{\sqrt[3]{(3 \times 3 \times 3)\times (3 \times 3 \times 3)}}{{\sqrt[3]{(11 \times 11 \times 11)}}}\\[1em] = -\dfrac{3 \times 3}{11}\\[1em] = -\dfrac{9}{11}3−1331729=−3−13313729=−3(11×11×11)3(3×3×3)×(3×3×3)=−113×3=−119
Hence, 729−13313=−911\sqrt[3]{\dfrac{729}{-1331}} = {-\dfrac{9}{11}}3−1331729=−119
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