To multiply and simplify the given expression [tex]\( \sqrt{6}(x + \sqrt{11}) \)[/tex], follow these steps:
1. Distribute [tex]\( \sqrt{6} \)[/tex] across the terms inside the parenthesis:
[tex]\[
\sqrt{6}(x + \sqrt{11}) = \sqrt{6} \cdot x + \sqrt{6} \cdot \sqrt{11}
\][/tex]
2. Simplify the product of radicals:
[tex]\[
\sqrt{6} \cdot x = \sqrt{6}x
\][/tex]
[tex]\[
\sqrt{6} \cdot \sqrt{11} = \sqrt{6 \cdot 11}
\][/tex]
3. Multiply the numbers inside the second radical:
[tex]\[
\sqrt{6 \cdot 11} = \sqrt{66}
\][/tex]
4. Combine the simplified terms into a single expression:
[tex]\[
\sqrt{6}x + \sqrt{66}
\][/tex]
So the simplified form of the expression [tex]\( \sqrt{6}(x + \sqrt{11}) \)[/tex] is:
[tex]\[
\sqrt{6}x + \sqrt{66}
\][/tex]
This is the exact answer, using radicals as needed.
