To solve the problem [tex]\(4 \sqrt{6} + 5 \sqrt{6}\)[/tex] and simplify by collecting like radical terms, follow these steps:
1. Identify the like radical terms:
In the expression [tex]\(4 \sqrt{6} + 5 \sqrt{6}\)[/tex], both terms contain the same radical part, which is [tex]\(\sqrt{6}\)[/tex].
2. Combine the coefficients of the like radicals:
Since the radical part ([tex]\(\sqrt{6}\)[/tex]) is common to both terms, you can add the coefficients (the numbers multiplying the radicals) together.
- The coefficient of the first term is 4.
- The coefficient of the second term is 5.
3. Perform the arithmetic with the coefficients:
Add the coefficients:
[tex]\[
4 + 5 = 9
\][/tex]
4. Rewrite the combined term:
Attach the sum of the coefficients to the common radical part:
[tex]\[
9 \sqrt{6}
\][/tex]
So, the simplified form of the expression [tex]\(4 \sqrt{6} + 5 \sqrt{6}\)[/tex] is [tex]\(9 \sqrt{6}\)[/tex].
Thus, the answer is:
[tex]\[
\boxed{9 \sqrt{6}}
\][/tex]
