To combine the radicals [tex]\(-2 \sqrt{13} + 19 \sqrt{13}\)[/tex], follow these steps:
1. Identify the numerical coefficients and the common radical part:
- The first term is [tex]\(-2 \sqrt{13}\)[/tex].
- The second term is [tex]\(19 \sqrt{13}\)[/tex].
Here, both terms have the same radical part, [tex]\(\sqrt{13}\)[/tex].
2. Combine the numerical coefficients while keeping the radical part constant:
- The coefficient of the first term is [tex]\(-2\)[/tex].
- The coefficient of the second term is [tex]\(19\)[/tex].
Combine these coefficients:
[tex]\[
-2 + 19 = 17
\][/tex]
3. Attach the common radical part to the simplified coefficient:
Using the combined coefficient and the shared radical part:
[tex]\[
17 \sqrt{13}
\][/tex]
So, [tex]\(-2 \sqrt{13} + 19 \sqrt{13}\)[/tex] simplifies to [tex]\(17 \sqrt{13}\)[/tex].
Therefore, the correct answer is:
[tex]\[
17 \sqrt{13}
\][/tex]
