Resolve the above answer in step by step for better understanding 

Certainly! Let's break down the process of finding the cube root of \( 6859 \) step by step:

### Step-by-Step Solution to Find \( \sqrt[3]{6859} \):

1. **Understanding the Problem:**
   - We need to find a number \( x \) such that \( x^3 = 6859 \).

2. **Prime Factorization (Optional for Understanding):**
   - Sometimes, breaking the number down into its prime factors can help, but for larger numbers, recognizing patterns or using known cubes is more efficient.

3. **Checking Smaller Cubes:**
   - We start by recognizing or checking if \( 6859 \) is a perfect cube.
   - \( 1^3 = 1 \)
   - \( 2^3 = 8 \)
   - \( 3^3 = 27 \)
   - \( 4^3 = 64 \)
   - \( 5^3 = 125 \)
   - \( 6^3 = 216 \)
   - \( 7^3 = 343 \)
   - \( 8^3 = 512 \)
   - \( 9^3 = 729 \)
   - \( 10^3 = 1000 \)
   - \( 11^3 = 1331 \)
   - \( 12^3 = 1728 \)
   - \( 13^3 = 2197 \)
   - \( 14^3 = 2744 \)
   - \( 15^3 = 3375 \)
   - \( 16^3 = 4096 \)
   - \( 17^3 = 4913 \)
   - \( 18^3 = 5832 \)
   - \( 19^3 = 6859 \)

4. **Verification:**
   - We find that \( 19^3 = 6859 \).
   - Therefore, \( 19 \) is the cube root of \( 6859 \).

5. **Final Answer:**
   - \[
   \sqrt[3]{6859} = 19
   \]

### Verification Calculation:
   - To verify, let's calculate \( 19^3 \):
     \[
     19 \times 19 \times 19 = 361 \times 19 = 6859
     \]

### Conclusion:
The cube root of \( 6859 \) is \( 19 \).

Would you like further details or have any questions about this calculation?

Here are some additional questions you might be interested in:
1. How do you solve quadratic equations?
2. What is the derivative of \( f(x) = x^3 + 3x^2 + 2x + 1 \)?
3. Can you explain the Pythagorean theorem?
4. How do you calculate the area of a circle?
5. What are the properties of logarithms?

**Tip:** When finding cube roots, it can be useful to remember common cubes or use a calculator for verification.

Learn how to find the cube root of 6859 with a detailed step-by-step solution. This problem covers cube roots and prime factorization, providing a comprehensive approach to solving cube root problems. Suitable for students in Grades 7-9.

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