Question

How can you write the expression with a rationalized denominator?See image

Answer 1

Okay, here we have this:

Considering the provided expression, we are going to rationalize the denominator, so we obtain the following:

`\begin{gathered} \frac{\sqrt[3]{3}}{\sqrt[3]{4}} \\ =\frac{\sqrt[3]{3}\cdot\sqrt[3]{4^2}}{\sqrt[3]{4}\cdot\sqrt[3]{4^2}} \\ =\frac{\sqrt[3]{3}\cdot\sqrt[3]{2^4}}{4^{(1)/(3)+(2)/(3)}} \\ =\frac{\sqrt[3]{3}\cdot2^{(4)/(3)}}{2^2} \\ =\frac{\sqrt[3]{3}\sqrt[3]{2}}{2} \\ =\frac{\sqrt[3]{6}}{2} \end{gathered}`

Finally we obtain that the correct answer is the second option.