To cancel out a cube root in the denominator, you typically rationalize the denominator by eliminating the cube root. Here are the steps:

1. Understand the Cube Root in the Denominator: If the denominator is $\sqrt[3]{a}$, the goal is to make it a rational number (remove the cube root).

2. Multiply by a Form That Creates a Cube: To remove $\sqrt[3]{a}$, multiply the numerator and denominator by $\sqrt[3]{a^2}$. This works because: [ \sqrt[3]{a} \cdot \sqrt[3]{a^2} = \sqrt[3]{a^3} = a. ]

3. Simplify the Expression: After multiplying, simplify the numerator and denominator.

Example:

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

• Multiply numerator and denominator by $\sqrt[3]{2^2}$: [ \frac{1}{\sqrt[3]{2}} \cdot \frac{\sqrt[3]{2^2}}{\sqrt[3]{2^2}} = \frac{\sqrt[3]{2^2}}{\sqrt[3]{2^3}} = \frac{\sqrt[3]{4}}{2}. ]

The denominator is now rationalized.

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Key Points:

• You multiply by the power that complements the cube to make a perfect cube in the denominator.
• Ensure you balance the numerator and denominator to maintain equality.

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Would you like a more detailed example or explanation?

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Related Questions:

1. What is the difference between rationalizing square roots and cube roots?
2. How do you simplify cube roots in the numerator?
3. Can you explain how to handle fractional cube roots?
4. How do you handle cube roots with variables?
5. What is the general formula for rationalizing cube root denominators?

Tip:

When rationalizing cube roots, always check if the root can already simplify before multiplying by additional terms.