Question

Multiply. Write your answer in simplest form
square root 2( 5 + square root 2)

Answer 1

To multiply \(\sqrt{2}(5 + \sqrt{2})\), distribute \(\sqrt{2}\) to both terms inside the parentheses:

\[
\sqrt{2} \cdot 5 + \sqrt{2} \cdot \sqrt{2}
\]

Calculating each term:

1. \(\sqrt{2} \cdot 5 = 5\sqrt{2}\)
2. \(\sqrt{2} \cdot \sqrt{2} = 2\)

Now, combine the results:

\[
5\sqrt{2} + 2
\]

Thus, the answer in simplest form is:

\[
\boxed{5\sqrt{2} + 2}
\]