What is the cube root of 189?
Understand the Problem
The question is asking to calculate the cube root of 189, which is finding a number that, when multiplied by itself twice, equals 189.
Answer
The cube root of 189 is approximately \( \sqrt[3]{189} \approx 5.821 \).
Answer for screen readers
The cube root of 189 is approximately ( \sqrt[3]{189} \approx 5.821 ).
Steps to Solve
- Identify the cube root notation
The cube root of a number $x$ is denoted as $\sqrt[3]{x}$. In this case, we want to find $\sqrt[3]{189}$.
- Estimate the cube root
To estimate $\sqrt[3]{189}$, we can find the cubes of integers around the value. We compute:
- $5^3 = 125$
- $6^3 = 216$
Since $125 < 189 < 216$, we know that $\sqrt[3]{189}$ is between 5 and 6.
- Use a calculator for precision
We can use a calculator to find a more precise value for $\sqrt[3]{189}$.
When we input this into a calculator, we find:
$$\sqrt[3]{189} \approx 5.821$$
- Conclusion
Thus, we can conclude that the cube root of 189 is approximately 5.821.
The cube root of 189 is approximately ( \sqrt[3]{189} \approx 5.821 ).
More Information
The cube root offers a way to determine the side length of a cube whose volume is 189 cubic units. This value can be useful in various applications such as geometry and physics.
Tips
- Misinterpreting the cube root as a square root; remember that a cube root finds a number that, when multiplied by itself three times, equals the given number.
- Rounding errors; ensure calculations with decimals are accurate, especially when using a calculator.
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