What is the cube root of 1/27?
Understand the Problem
The question is asking for the cube root of the fraction 1/27. To solve this, we need to determine which number, when multiplied by itself three times, would equal 1/27. The cube root operation can be applied to both the numerator and the denominator separately.
Answer
The cube root of $\frac{1}{27}$ is $\frac{1}{3}$.
Answer for screen readers
The cube root of $\frac{1}{27}$ is $\frac{1}{3}$.
Steps to Solve
- Apply the Cube Root to the Fraction
We want to find the cube root of the fraction $\frac{1}{27}$. This can be expressed as:
$$ \sqrt[3]{\frac{1}{27}} $$
Using the property of cube roots, we can separate the numerator and denominator:
$$ \frac{\sqrt[3]{1}}{\sqrt[3]{27}} $$
- Calculate the Cube Root of the Numerator
The cube root of 1 is straightforward:
$$ \sqrt[3]{1} = 1 $$
- Calculate the Cube Root of the Denominator
Now, we calculate the cube root of 27:
$$ \sqrt[3]{27} = 3 $$
This is because $3 \times 3 \times 3 = 27$.
- Combine the Results
Now that we have both parts, we can combine them:
$$ \frac{1}{3} $$
The cube root of $\frac{1}{27}$ is $\frac{1}{3}$.
More Information
Finding the cube root involves determining what number, when multiplied by itself three times, equals the original number. For fractions, you can separately take the root of the numerator and the denominator. In this case, $27$ is a perfect cube because $3^3 = 27$.
Tips
- Miscalculating the cube root of the denominator. Remember that $3 \times 3 \times 3 = 27$, and not confusing it with any other operation.
- Not separating the fraction properly when taking the cube root.
