Simplify:$ 2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500} $.

Given:

\( 2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500} \).

To do:

We have to simplify \( 2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500} \).

Solution:

$2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}=2\sqrt[3]{4}+7\sqrt[3]{4\times8}+\sqrt[3]{125\times4}$

$=2\sqrt[3]{4}+7\sqrt[3]{4\times2^3}+\sqrt[3]{5^3\times4}$

$=2\sqrt[3]{4}+7\times2\sqrt[3]{4}+5\sqrt[3]{4}$

$=2\sqrt[3]{4}+14\sqrt[3]{4}+5\sqrt[3]{4}$

$=21\sqrt[3]{4}$

Therefore,

$2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}=21\sqrt[3]{4}$.

Tutorialspoint

Updated on: 10-Oct-2022

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