To find the sum of the expressions [tex]\(6 y \sqrt{a} + 7 y \sqrt{a}\)[/tex], we can use the following steps:
1. Identify Like Terms:
Both terms [tex]\(6 y \sqrt{a}\)[/tex] and [tex]\(7 y \sqrt{a}\)[/tex] have the same variables and radical part, which means they are like terms. Like terms can be combined by adding their coefficients.
2. Add the Coefficients:
The coefficients of the terms are 6 and 7. Add these coefficients together:
[tex]\[
6 + 7 = 13
\][/tex]
3. Retain the Common Variable and Radical Part:
Since we are combining like terms, the variable [tex]\( y \)[/tex] and the radical part [tex]\( \sqrt{a} \)[/tex] remain the same.
4. Write the Result:
Combine the sum of the coefficients with the common variable and radical part to form the final expression:
[tex]\[
13 y \sqrt{a}
\][/tex]
Therefore, the correct answer is [tex]\(\boxed{13 y \sqrt{a}}\)[/tex].
