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Question

Simplify: $6 \sqrt[3]{32} + 2 \sqrt[3]{108}$
$18 \sqrt[3]{2}$
$36 \sqrt[3]{2}$
$32$
$18 \sqrt[3]{4}$

A

36 \sqrt[3]{2}

B

18 \sqrt[3]{2}

C

18 \sqrt[3]{4}

D

32

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Solution

Verified by Toppr

The given expression can be simplified as follows:
$6 \sqrt[3]{32} + 2 \sqrt[3]{108}$
$\Rightarrow 6 \sqrt[3]{2^{3} \times 4} + 2 \sqrt[3]{3^{3} \times 4}$
$\Rightarrow 6 \times 2 \sqrt[3]{4} + 2 \times 3 \sqrt[3]{4}$
$\Rightarrow 12 \sqrt[3]{4} + 6 \sqrt[3]{4}$
$\Rightarrow 18 \sqrt[3]{4}$

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