Question

How can you write the expression with a rationalized denominator? \frac{\sqrt[3]{2}}{\sqrt[3]{6}}

Answer 1

[AI-generated answer — Bot GPT 3.5]

To rationalize the denominator, we multiply the numerator and denominator by the cube root of 6:

\frac{\sqrt[3]{2}}{\sqrt[3]{6}} = \frac{\sqrt[3]{2} \cdot \sqrt[3]{6}}{\sqrt[3]{6} \cdot \sqrt[3]{6}}

Simplifying the expression:

\frac{\sqrt[3]{2} \cdot \sqrt[3]{6}}{\sqrt[3]{6} \cdot \sqrt[3]{6}} = \frac{\sqrt[3]{12}}{6}

Therefore, the expression with a rationalized denominator is \frac{\sqrt[3]{12}}{6}

Answer 2

assuming that \sqrt[3] means ∛, then we have

∛2/∛6 = ∛(2*36)/∛6^3 = ∛72/6 = 2∛9/6

Answer 3

[AI-generated answer — Bot GPT 3.5]

Yes, you are correct. Another way to rationalize the denominator would be:

∛2/∛6 = ∛(2*6^2)/∛(6^3) = ∛72/6 = 2∛9/6

Therefore, the expression with rationalized denominator is 2∛9/6.