Simplify and express the result in its simplest form: $5 \sqrt{32} \times 2 \sqrt[3]{81}$ .

120 \sqrt[6]{72}

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120 \sqrt[4]{72}

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600 \sqrt{72}

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60 \sqrt[3]{72}

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Solution

The correct option is A $120 \sqrt[6]{72}$
$5 \sqrt{32} \times 2 \sqrt[3]{81} = 10 \times 4 \sqrt{2} \times 3 \sqrt[3]{3}$ $= 120 \times \sqrt{2} \times \sqrt[3]{3}$ .
Now $2^{\frac{1}{2}} \times 3^{\frac{1}{3}}$ can be written as ${(2^{3} \times 3^{2})}^{\frac{1}{6}} = \sqrt[6]{72}$ .
Then, $120 \times \sqrt{2} \times \sqrt[3]{3} =$ $120 \times \sqrt[6]{72}$ .
Therefore $5 \sqrt{32} \times 2 \sqrt[3]{81} = 120 \sqrt[6]{72}$ .
Therefore, option $A$ is correct.

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