The correct option is C 36√(2) =3× ( 2^5 )^1/3× 3× ( 2^2 )^1/3 =3× 3× 2^5/3× 2^2/3 =3× 3× 2^5/3+2/3 =3× 3× 2^7/3 =3× 3×2^6/3×2^1/ ...

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Deducing Formula for (x-y)^2

Simplify 3....

Question

Simplify $3. \sqrt[3]{32} \times 3. \sqrt[3]{4}$

9 \sqrt[3]{2}

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32 \sqrt[3]{2}

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36 \sqrt[3]{2}

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18 \sqrt[3]{2}

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Solution

The correct option is C $36 \sqrt[3]{2}$
$= 3 \times {(2^{5})}^{\frac{1}{3}} \times 3 \times {(2^{2})}^{\frac{1}{3}}$
$= 3 \times 3 \times 2^{\frac{5}{3}} \times 2^{\frac{2}{3}}$
$= 3 \times 3 \times 2^{\frac{5}{3} + \frac{2}{3}}$
$= 3 \times 3 \times 2^{\frac{7}{3}}$
$= 3 \times 3 \times 2^{\frac{6}{3}} \times 2^{\frac{1}{3}}$
$= 3 \times 3 \times 2^{2} \times 2^{\frac{1}{3}}$
$= 36 \times 2^{\frac{1}{3}}$
$= 36 \sqrt[3]{2}$

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