Which of the following is equal to 9?

Options

A. `sqrt729`
B. `3sqrt729`
C. `root3(729)`
D. `(3)^(3)`

Answer

To solve the question "Which of the following is equal to 9?", we will evaluate each option step by step.

### Step-by-Step Solution:

1. **Evaluate Option A: 729**
- We know that \( 729 = 9 \times 9 \times 9 \) (or \( 9^3 \)).
- To find the cube root of \( 729 \), we can express it as:
\[ \sqrt[3]{729} = \sqrt[3]{9^3} = 9 \]
- Therefore, \( \sqrt[3]{729} = 9 \).
- **Conclusion:** This option is equal to 9.

2. **Evaluate Option B: \( 3 \sqrt{729} \)**
- First, we need to find \( \sqrt{729} \).
- Since \( 729 = 27 \times 27 \) (or \( 27^2 \)), we have:
\[ \sqrt{729} = 27 \]
- Now, substituting back into the expression:
\[ 3 \sqrt{729} = 3 \times 27 = 81 \]
- **Conclusion:** This option is not equal to 9.

3. **Evaluate Option C: Cube root of 729**
- We already established that \( 729 = 9^3 \).
- Therefore, the cube root of \( 729 \) is:
\[ \sqrt[3]{729} = \sqrt[3]{9^3} = 9 \]
- **Conclusion:** This option is equal to 9.

4. **Evaluate Option D: \( 3^3 \)**
- We calculate \( 3^3 \):
\[ 3^3 = 3 \times 3 \times 3 = 27 \]
- **Conclusion:** This option is not equal to 9.

### Final Answer:
The only option that is equal to 9 is **Option C: Cube root of 729**.