What is the cube root of 0.125?
Understand the Problem
The question is asking for the cube root of the number 0.125, which involves finding a number that, when multiplied by itself twice (three times total), equals 0.125.
Answer
The cube root of 0.125 is $\frac{1}{2}$.
Answer for screen readers
The cube root of 0.125 is $\frac{1}{2}$.
Steps to Solve
- Identify the cube root requirement
We are looking to find a number $x$ such that when we cube it, we get 0.125. This can be expressed as:
$$ x^3 = 0.125 $$
- Convert 0.125 to a fraction
To make calculations easier, let's convert 0.125 into a fraction.
$$ 0.125 = \frac{125}{1000} $$
We can simplify this fraction:
$$ 0.125 = \frac{1}{8} $$
- Set up the cube root equation
Now we want to find $x$ such that:
$$ x^3 = \frac{1}{8} $$
- Apply the cube root operation
To isolate $x$, we take the cube root of both sides:
$$ x = \sqrt[3]{\frac{1}{8}} $$
- Solve the cube root
The cube root of $\frac{1}{8}$ can be computed by finding the cube root of both the numerator and the denominator:
$$ x = \frac{\sqrt[3]{1}}{\sqrt[3]{8}} = \frac{1}{2} $$
The cube root of 0.125 is $\frac{1}{2}$.
More Information
The number $\frac{1}{2}$ is significant because it's the exact value that, when multiplied by itself three times, gives the original number 0.125. This helps in applications involving volume calculations in cubic measurements.
Tips
- Confusing cube roots with square roots. Remember, you want the number that, when multiplied by itself three times, equals the original number.
- Forgetting to simplify fractions, which can lead to incorrect results.
