Question

8square root 11(4 +7square root 7)

Answer 1

To simplify the expression \(8\sqrt{11}(4 + 7\sqrt{7})\), you can distribute \(8\sqrt{11}\) to each term inside the parentheses.

Here’s how to do that step by step:

1. **Distribute \(8\sqrt{11}\)**:
\[
8\sqrt{11} \times 4 + 8\sqrt{11} \times 7\sqrt{7}
\]

2. **Calculate each term**:
- The first term:
\[
8\sqrt{11} \times 4 = 32\sqrt{11}
\]
- The second term:
\[
8\sqrt{11} \times 7\sqrt{7} = 56\sqrt{77} \quad (\text{since } \sqrt{11} \times \sqrt{7} = \sqrt{77})
\]

3. **Combine the results**:
\[
32\sqrt{11} + 56\sqrt{77}
\]

Thus, the simplified expression is:
\[
\boxed{32\sqrt{11} + 56\sqrt{77}}
\]