To cube root a fraction, you need to find the cube root of the numerator and the cube root of the denominator separately.
Understanding Cube Roots
A cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2 because 2 2 2 = 8.
Steps to Cube Root a Fraction
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Separate the Fraction: Consider the fraction as having a numerator (top part) and a denominator (bottom part).
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Cube Root the Numerator: Find the cube root of the numerator. This means finding a number that, when multiplied by itself three times, equals the numerator.
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Cube Root the Denominator: Find the cube root of the denominator. This means finding a number that, when multiplied by itself three times, equals the denominator.
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Form the New Fraction: Create a new fraction where the cube root of the numerator is the new numerator and the cube root of the denominator is the new denominator.
Example
Let's look at the example from the provided reference where you need to find the cube root of 8/27.
| Step | Action | Result |
|---|---|---|
| 1. | Separate the fraction | 8 / 27 |
| 2. | Cube root the numerator (8) | ∛8 = 2 |
| 3. | Cube root the denominator (27) | ∛27 = 3 |
| 4. | Form the new fraction | 2 / 3 |
Therefore, the cube root of 8/27 is 2/3. As the reference states: "So this is the cube root of the top piece divided by the cube root of the bottom. Piece just take the cube root of each piece. And the cube root of 8 is 2.. That's because 2 cubed is 8."
Key Points
- The cube root of a fraction can be found by taking the cube root of both the numerator and denominator.
- This method works for any fraction where both numerator and denominator have a perfect cube root.
- If a fraction has a numerator or denominator that doesn't have a perfect cube root, you may need to use approximation techniques or calculators.
