To estimate the value of \( \sqrt[3]{218} \), we can look for nearby perfect cubes and refine our estimate.

- \( 5^3 = 125 \)
- \( 6^3 = 216 \)
- \( 7^3 = 343 \)

Since \( 218 \) is very close to \( 216 \), we know that \( \sqrt[3]{218} \) will be slightly greater than 6.

To refine the estimate:

- Try \( 6.1^3 \):  
  \( 6.1^3 = 6.1 \times 6.1 \times 6.1 = 226.981 \)

This is too high. So, the cube root of 218 is a little less than 6.1.

Thus, the estimate for \( \sqrt[3]{218} \) is approximately **6.05**.

Would you like further details or a breakdown of how we can refine this estimate?

Here are some related questions to consider:
1. What are other ways to approximate cube roots manually?
2. How can we calculate cube roots using a calculator or software?
3. What are perfect cubes between 1 and 500?
4. How can we apply cube root approximations to real-life problems?
5. How do cube roots relate to solving cubic equations?

**Tip:** When estimating cube roots, finding the closest perfect cubes helps in narrowing down the value quickly.

Learn how to estimate the cube root of 218 by identifying nearby perfect cubes and refining the estimate. This step-by-step guide helps students understand the process of approximating cube roots, suitable for Grades 8-10.

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