`3sqrt(2744) div 7` is equal to

Options

A. 14
B. 2
C. 15
D. 8

Answer

To solve the expression \( 3\sqrt[3]{2744} \div 7 \), we will follow these steps:

### Step 1: Find the Cube Root of 2744
To find the cube root of 2744, we can factorize 2744.

- Start by dividing 2744 by 2:
\[ 2744 \div 2 = 1372 \]
- Divide 1372 by 2:
\[ 1372 \div 2 = 686 \]
- Divide 686 by 2:
\[ 686 \div 2 = 343 \]
- Now, divide 343 by 7:
\[ 343 \div 7 = 49 \]
- Divide 49 by 7:
\[ 49 \div 7 = 7 \]
- Finally, divide 7 by 7:
\[ 7 \div 7 = 1 \]

Thus, the prime factorization of 2744 is:
\[ 2744 = 2^3 \times 7^3 \]

### Step 2: Calculate the Cube Root
Now we can calculate the cube root:
\[ \sqrt[3]{2744} = \sqrt[3]{2^3 \times 7^3} = \sqrt[3]{2^3} \times \sqrt[3]{7^3} = 2 \times 7 = 14 \]

### Step 3: Multiply by 3
Now we multiply the cube root by 3:
\[ 3 \times \sqrt[3]{2744} = 3 \times 14 = 42 \]

### Step 4: Divide by 7
Finally, we divide by 7:
\[ \frac{42}{7} = 6 \]

### Final Answer
Thus, the value of \( 3\sqrt[3]{2744} \div 7 \) is:
\[ \boxed{6} \]

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