`3sqrt(1331) xx 3sqrt(216) + 3sqrt(729) + 3sqrt(64)` is equal to

Options

A. 78
B. 79
C. 15
D. 91

Answer

To solve the expression \( 3\sqrt[3]{1331} \times 3\sqrt[3]{216} + 3\sqrt[3]{729} + 3\sqrt[3]{64} \), we will simplify each term step by step.

### Step 1: Simplify each cube root
1. **Calculate \( \sqrt[3]{1331} \)**:
- \( 1331 = 11^3 \)
- Therefore, \( \sqrt[3]{1331} = 11 \)

2. **Calculate \( \sqrt[3]{216} \)**:
- \( 216 = 6^3 \)
- Therefore, \( \sqrt[3]{216} = 6 \)

3. **Calculate \( \sqrt[3]{729} \)**:
- \( 729 = 9^3 \)
- Therefore, \( \sqrt[3]{729} = 9 \)

4. **Calculate \( \sqrt[3]{64} \)**:
- \( 64 = 4^3 \)
- Therefore, \( \sqrt[3]{64} = 4 \)

### Step 2: Substitute back into the expression
Now we substitute these values back into the expression:
\[ 3\sqrt[3]{1331} \times 3\sqrt[3]{216} + 3\sqrt[3]{729} + 3\sqrt[3]{64} \]
becomes:
\[ 3 \times 11 \times 3 \times 6 + 3 \times 9 + 3 \times 4 \]

### Step 3: Calculate each term
1. **Calculate \( 3 \times 11 \times 3 \times 6 \)**:
- \( 3 \times 11 = 33 \)
- \( 33 \times 3 = 99 \)
- \( 99 \times 6 = 594 \)

2. **Calculate \( 3 \times 9 \)**:
- \( 3 \times 9 = 27 \)

3. **Calculate \( 3 \times 4 \)**:
- \( 3 \times 4 = 12 \)

### Step 4: Combine all terms
Now we combine all the results:
\[ 594 + 27 + 12 \]
Calculating this gives:
\[ 594 + 27 = 621 \]
\[ 621 + 12 = 633 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{633} \]