`(5sqrt(7)+2sqrt(7))(6sqrt(7)+3sqrt(7))=?`

Options

A. 401
B. 415
C. 417
D. 441

Explanation

To solve the expression \((5\sqrt{7} + 2\sqrt{7})(6\sqrt{7} + 3\sqrt{7})\), we can follow these steps:

### Step 1: Simplify the terms inside the parentheses
Combine like terms in each parenthesis:
\[ 5\sqrt{7} + 2\sqrt{7} = 7\sqrt{7} \]
\[ 6\sqrt{7} + 3\sqrt{7} = 9\sqrt{7} \]

### Step 2: Rewrite the expression
Now, substitute the simplified terms back into the expression:
\[ (7\sqrt{7})(9\sqrt{7}) \]

### Step 3: Multiply the coefficients and the square roots
Multiply the coefficients (7 and 9) and the square roots:
\[ 7 \times 9 = 63 \]
\[ \sqrt{7} \times \sqrt{7} = 7 \]

### Step 4: Combine the results
Now, multiply the results from the previous step:
\[ 63 \times 7 = 441 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{441} \]