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

  1. 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 $\sqrt[3]{189}$.

  1. 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.

  1. 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:

$$\sqrt[3]{189} \approx 5.821$$

  1. 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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