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Question Number 137582 by SOMEDAVONG last updated on 04/Apr/21

$$\mathrm{A}=\sqrt[3]{\frac{1}{3}(\sqrt[3]{2}-1){(\sqrt[3]{2}+1)}^3}$$

Answered by Ñï= last updated on 04/Apr/21

$$A=\sqrt[3]{\frac{1}{3}(\sqrt[3]{2}-1){(\sqrt[3]{2}+1)}^3}$$$$=\sqrt[3]{\frac{1}{3}(\sqrt[3]{4}-1){(\sqrt[3]{2}+1)}^2}=\sqrt[3]{\frac{1}{3}(\sqrt[3]{4}-1)(\sqrt[3]{4}+2\sqrt[3]{2}+1)}$$$$=\sqrt[3]{\frac{1}{3}(\sqrt[3]{16}+2\sqrt[3]{8}-2\sqrt[3]{2}+1)}=\sqrt[3]{\frac{1}{3}(2\sqrt[3]{2}+4-2\sqrt[3]{2}+1)}$$$$=\sqrt[3]{\frac{5}{3}}$$

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