The correct option is A 1/√(3) The value of √(12)÷(√(3) #10; #160;√(2)) is #10; √( 12 ) #160;√( 3 )√( 2 #10;) #160; #10; =√( ...

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Substitution Method to Remove Indeterminate Form

Simplify : ...

Question

Simplify :
$\sqrt[6]{12} \div (\sqrt{3} \times \sqrt[3]{2})$ .

\frac{1}{\sqrt[3]{3}}

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\frac{1}{\sqrt[4]{3}}

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\frac{1}{\sqrt[3]{4}}

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\frac{1}{\sqrt[2]{3}}

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Solution

The correct option is A $\frac{1}{\sqrt[3]{3}}$
The value of $\sqrt[6]{12} \div (\sqrt{3} \sqrt[3]{2})$ is
$\frac{\sqrt[6]{12}}{\sqrt{3} \sqrt[3]{2}}$
$= \frac{\sqrt[6]{12}}{{\sqrt{3}}^{\frac{1}{2}} {\sqrt{2}}^{\frac{1}{3}}}$
$= \frac{12^{\frac{1}{6}}}{3^{\frac{3}{6}} 2^{\frac{2}{6}}}$
$= \frac{12^{\frac{1}{6}}}{{(3^{3} \times 2^{2})}^{\frac{1}{6}}}$
$= {(\frac{12}{3^{3} \times 2^{2}})}^{\frac{1}{6}}$
$= {(\frac{3 \times 2^{2}}{3^{3} \times 2^{2}})}^{\frac{1}{6}}$
$= {(\frac{1}{3^{2}})}^{\frac{1}{6}}$
$= ⎛ ⎜ ⎜ ⎜ ⎝ \frac{1}{3^{\frac{2}{6}}} ⎞ ⎟ ⎟ ⎟ ⎠$
$= ⎛ ⎜ ⎜ ⎜ ⎝ \frac{1}{3^{\frac{1}{3}}} ⎞ ⎟ ⎟ ⎟ ⎠$
$= (\frac{1}{\sqrt[3]{3}})$

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