The correct option is A √(24) √(2)×√(3)×√(4) =2^ 1 / 2 nbsp;× 3^ 1 / 3 nbsp;× 2^ 2 / 4 nbsp; =2^ 1 / 2 nbsp;× 2^ 1 / 2 nbsp; ...

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Laws of Exponents for Real Numbers

Simplify : ...

Question

Simplify :
$\sqrt{2} \times \sqrt[3]{3} \times \sqrt[4]{4}$ .

\sqrt[3]{12}

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\sqrt[3]{24}

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\sqrt[3]{20}

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\sqrt[3]{25}

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Solution

The correct option is A $\sqrt[3]{24}$
$\sqrt{2} \times \sqrt[3]{3} \times \sqrt[4]{4}$
$= 2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 2^{\frac{2}{4}}$
$= 2^{\frac{1}{2}} \times 2^{\frac{1}{2}} \times 3^{\frac{1}{3}}$
$= 2 \times 3^{\frac{1}{3}}$
$= 2^{\frac{3}{3}} \times 3^{\frac{1}{3}}$
$= \sqrt[3]{2^{3}} \times \sqrt[3]{3}$
$= \sqrt[3]{8 \times 3}$
$= \sqrt[3]{24}$

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