Question

Multiply.
V2(12+V3)
Simplify your answer as much as possible.

Answer 1

To multiply \( \sqrt{2}(12 + \sqrt{3}) \), we will distribute \( \sqrt{2} \) across the terms inside the parentheses.

\[
\sqrt{2}(12 + \sqrt{3}) = \sqrt{2} \cdot 12 + \sqrt{2} \cdot \sqrt{3}
\]

Calculating each term:

1. \( \sqrt{2} \cdot 12 = 12\sqrt{2} \)
2. \( \sqrt{2} \cdot \sqrt{3} = \sqrt{2 \cdot 3} = \sqrt{6} \)

Now combine the terms:

\[
12\sqrt{2} + \sqrt{6}
\]

Thus, the simplified answer is:

\[
\boxed{12\sqrt{2} + \sqrt{6}}
\]