What is the value of the cube root of 4913? Use an estimation method to find the cube root.

To find the cube root of 4913 using estimation, we can start by identifying two perfect cubes that are close to 4913. This will help us narrow down our guess for the cube root.

Identifying Nearby Perfect Cubes

First, let's recall some perfect cubes:

• 1³ = 1
• 2³ = 8
• 3³ = 27
• 4³ = 64
• 5³ = 125
• 6³ = 216
• 7³ = 343
• 8³ = 512
• 9³ = 729
• 10³ = 1000
• 11³ = 1331
• 12³ = 1728
• 13³ = 2197
• 14³ = 2744
• 15³ = 3375
• 16³ = 4096
• 17³ = 4913
• 18³ = 5832

Finding the Range

From this list, we can see that:

• 16³ = 4096
• 17³ = 4913
• 18³ = 5832

Since 4913 is equal to 17³, we can conclude that the cube root of 4913 is exactly 17.

Verification

To ensure our estimation is correct, we can verify by calculating:

• 17 × 17 = 289
• 289 × 17 = 4913

This confirms that our estimation method was accurate, as we arrived at the original number.

Conclusion

In summary, the cube root of 4913 is 17. By identifying nearby perfect cubes, we effectively narrowed down our estimation and confirmed our result through multiplication. This method not only provides the answer but also reinforces understanding of cube roots and their properties.