Multiply

V6(v2-2v7)
Simplify as much as possible

1 answer

To multiply \( \sqrt{6}(\sqrt{2} - 2\sqrt{7}) \), we'll distribute \( \sqrt{6} \) to each term inside the parentheses:

\[ \sqrt{6} \cdot \sqrt{2} - \sqrt{6} \cdot 2\sqrt{7} \]

Now, we can simplify each term:

  1. For the first term: \[ \sqrt{6} \cdot \sqrt{2} = \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3} \]

  2. For the second term: \[ \sqrt{6} \cdot 2\sqrt{7} = 2\sqrt{42} \]

Putting it all together, we have:

\[ 2\sqrt{3} - 2\sqrt{42} \]

We can factor out the common factor of 2:

\[ 2(\sqrt{3} - \sqrt{42}) \]

Therefore, the simplified expression is:

\[ \boxed{2(\sqrt{3} - \sqrt{42})} \]