Question

-6square root 3(8 - square root 26)

Answer 1

To simplify the expression \(-6\sqrt{3}(8 - \sqrt{26})\), you can distribute \(-6\sqrt{3}\) to each term inside the parentheses:

\[
-6\sqrt{3}(8 - \sqrt{26}) = -6\sqrt{3} \cdot 8 + -6\sqrt{3} \cdot (-\sqrt{26})
\]

Calculating each term:

1. \(-6\sqrt{3} \cdot 8 = -48\sqrt{3}\)
2. \(-6\sqrt{3} \cdot (-\sqrt{26}) = 6\sqrt{3} \cdot \sqrt{26} = 6\sqrt{78}\)

Now combine the results:

\[
-6\sqrt{3}(8 - \sqrt{26}) = -48\sqrt{3} + 6\sqrt{78}
\]

Thus, the simplified expression is:

\[
-48\sqrt{3} + 6\sqrt{78}
\]