Question: Simplify: $\dfrac{5 \sqrt[3]{81} - 2\sqrt[3]{24}}{2 \sqrt[3]{48} + 3\sqrt[3]{162}}$


Solution:
Given,

$= \dfrac{5 \sqrt[3]{81} - 2\sqrt[3]{24}}{2 \sqrt[3]{48} + 3\sqrt[3]{162}}$

$= \dfrac{5 \sqrt[3]{3^3 × 3} - 2\sqrt[3]{2^3 × 3}}{2 \sqrt[3]{2^3 × 6} + 3\sqrt[3]{3^3×6}}$

$= \dfrac{5 × 3 \sqrt[3]{3} - 2×2 \sqrt[3]{3}}{2×2 \sqrt[3]{6} + 3×3 \sqrt[3]{6}}$

$= \dfrac{15 \sqrt[3]{3} - 4\sqrt[3]{3}}{4 \sqrt[3]{6} + 9\sqrt[3]{6}}$

$= \dfrac{(15-4) \sqrt[3]{3}}{(4+9)\sqrt[3]{6}}$

$= \dfrac{11 \sqrt[3]{3}}{13 \sqrt[3]{6}}$

$= \dfrac{11}{13} × \sqrt[3]{\dfrac{3}{6}}$

$= \dfrac{11}{13} × \sqrt[3]{\dfrac{1}{2}}$

$= \dfrac{11 × \sqrt[3]{1}}{13 × \sqrt[3]{2}}$

$= \dfrac{11}{13 \sqrt[3]{2}}$
= Answer

Related Notes and Solutions:

Here is the website link to the notes of Indices.

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