Evaluate `root3(9261)`

Options

A. `23`
B. `22`
C. `21`
D. `27`

Answer

To evaluate the cube root of 9261, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Problem**: We need to find the cube root of 9261, which is denoted as \( \sqrt[3]{9261} \).

2. **Factorization**: We will try to find a number that, when multiplied by itself three times (cubed), gives us 9261. We can start by checking if 9261 is a perfect cube.

3. **Trial and Error**: We can try different integers to see if they yield 9261 when cubed. After testing various numbers, we find that:
\[ 21 \times 21 \times 21 = 9261 \]

4. **Expressing in Exponential Form**: Since \( 21 \times 21 \times 21 = 21^3 \), we can rewrite our expression:
\[ \sqrt[3]{9261} = \sqrt[3]{21^3} \]

5. **Applying the Cube Root**: The cube root of \( 21^3 \) can be simplified using the property of exponents:
\[ \sqrt[3]{21^3} = 21^{3 \times \frac{1}{3}} = 21^1 = 21 \]

6. **Final Answer**: Therefore, the cube root of 9261 is:
\[ \sqrt[3]{9261} = 21 \]

### Conclusion:
The cube root of 9261 is 21.

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