Question

3square root 3(10square root 22 + square root 2)

Answer 1

To simplify the expression \( 3\sqrt{3}(10\sqrt{22} + \sqrt{2}) \), you can distribute \( 3\sqrt{3} \) across the terms inside the parentheses.

\[
3\sqrt{3} \cdot (10\sqrt{22} + \sqrt{2}) = 3\sqrt{3} \cdot 10\sqrt{22} + 3\sqrt{3} \cdot \sqrt{2}
\]

Now, simplify each term:

1. For the first term:
\[
3\sqrt{3} \cdot 10\sqrt{22} = 30\sqrt{3 \cdot 22} = 30\sqrt{66}
\]

2. For the second term:
\[
3\sqrt{3} \cdot \sqrt{2} = 3\sqrt{3 \cdot 2} = 3\sqrt{6}
\]

Now, combine the two results:
\[
30\sqrt{66} + 3\sqrt{6}
\]

So, the simplified form of the expression \( 3\sqrt{3}(10\sqrt{22} + \sqrt{2}) \) is:

\[
\boxed{30\sqrt{66} + 3\sqrt{6}}
\]