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Question

Write in ascending order:
$$ 2 \sqrt[3]{5} $$ and $$ 3 \sqrt[3]{2} $$

Solution
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$$ 2 \sqrt[3]{5}=\sqrt[3]{2\times2\times2 \times 5}=\sqrt[3]{40}, 3 \sqrt[3]{2}=\sqrt[3]{3\times3\times3 \times 2}=\sqrt[3]{54} $$
We know that, $$ 40<54 $$ $$ \Rightarrow \sqrt[3]{40}<\sqrt[3]{54} $$
$$ \Rightarrow 2 \sqrt[3]{5}<3 \sqrt[3]{2} $$

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