Simplify the following expression
`7 sqrt48 +7 sqrt(147)`

Options

A. `76 sqrt3`
B. `77 sqrt7`
C. `77sqrt3`
D. `76 sqrt7`

Answer

To simplify the expression \( 7 \sqrt{48} + 7 \sqrt{147} \), we can follow these steps:

### Step 1: Factor out the common term
The expression can be factored by taking out the common factor of \( 7 \):
\[ 7 \sqrt{48} + 7 \sqrt{147} = 7 (\sqrt{48} + \sqrt{147}) \]

**Hint:** Look for common factors in the terms to simplify the expression.

### Step 2: Simplify each square root
Now, we simplify \( \sqrt{48} \) and \( \sqrt{147} \) separately.

**For \( \sqrt{48} \):**
\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]

**For \( \sqrt{147} \):**
\[ \sqrt{147} = \sqrt{49 \times 3} = \sqrt{49} \times \sqrt{3} = 7\sqrt{3} \]

**Hint:** Factor the numbers under the square root to find perfect squares.

### Step 3: Substitute back into the expression
Now substitute the simplified square roots back into the expression:
\[ 7 (\sqrt{48} + \sqrt{147}) = 7 (4\sqrt{3} + 7\sqrt{3}) \]

### Step 4: Combine like terms
Combine the terms inside the parentheses:
\[ 4\sqrt{3} + 7\sqrt{3} = (4 + 7)\sqrt{3} = 11\sqrt{3} \]

### Step 5: Final multiplication
Now, multiply by the factor we took out earlier:
\[ 7 (11\sqrt{3}) = 77\sqrt{3} \]

### Final Answer:
Thus, the simplified expression is:
\[ \boxed{77\sqrt{3}} \]