Question

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Answer 1

QUESTION:

$\sqrt[3]{16} + \sqrt[3]{54} + \sqrt[3]{192} - \sqrt[3]{375}$

ANSWER:

$5 \sqrt[3]{2} - \sqrt[3]{3}$

TO FIND:

$\sqrt[3]{16} + \sqrt[3]{54} + \sqrt[3]{192} - \sqrt[3]{375}$

EXPLANATION:

$\sqrt[3]{16} + \sqrt[3]{54} + \sqrt[3]{192} - \sqrt[3]{375} \\ \\ \sqrt[3]{16} = \sqrt[3]{2 \times 2 \times 2 \times 2} = 2\sqrt[3]{2} \\ \\ \sqrt[3]{54} = \sqrt[3]{3 \times 3 \times 3 \times 2} = 3\sqrt[3]{2} \\ \\ \sqrt[3]{192} = \sqrt[3]{4 \times 4 \times 4 \times 3} = 4\sqrt[3]{3} \\ \\ - \sqrt[3]{375} = - \sqrt[3]{5 \times 5 \times 5 \times 3} = - 5\sqrt[3]{3} \\ \\ Add \: the \: four \: terms \\ \\ 2\sqrt[3]{2} + 3\sqrt[3]{2} + 4\sqrt[3]{3} - 5\sqrt[3]{3} \\ \\ 5 \sqrt[3]{2} - \sqrt[3]{3}$

$\sqrt[3]{16} + \sqrt[3]{54} + \sqrt[3]{192} - \sqrt[3]{375} =5 \sqrt[3]{2} - \sqrt[3]{3}$