Multiply.

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

1 answer

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:

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