Question

-8square root 3(6 - 6square root 11)

Answer 1

To simplify the expression \(-8\sqrt{3}(6 - 6\sqrt{11})\), you can distribute \(-8\sqrt{3}\) to both terms inside the parentheses:

1. Multiply \(-8\sqrt{3}\) by \(6\):
\[
-8\sqrt{3} \cdot 6 = -48\sqrt{3}
\]

2. Multiply \(-8\sqrt{3}\) by \(-6\sqrt{11}\):
\[
-8\sqrt{3} \cdot -6\sqrt{11} = 48\sqrt{33} \quad (\text{since } - \times - = +)
\]

Now combine both results:
\[
-48\sqrt{3} + 48\sqrt{33}
\]

Thus, the simplified form of the expression is:
\[
48\sqrt{33} - 48\sqrt{3}
\]