To find the sum of the terms [tex]\(-3 y \sqrt{13}\)[/tex] and [tex]\(4 y \sqrt{13}\)[/tex], follow these steps:
1. Identify the like terms:
- Both terms involve the variable [tex]\(y\)[/tex] and the irrational number [tex]\(\sqrt{13}\)[/tex].
2. Combine the coefficients of [tex]\(\sqrt{13}\)[/tex]:
- The coefficient of [tex]\(\sqrt{13}\)[/tex] in the first term is [tex]\(-3\)[/tex].
- The coefficient of [tex]\(\sqrt{13}\)[/tex] in the second term is [tex]\(4\)[/tex].
3. Add the coefficients:
[tex]\[
-3 + 4 = 1
\][/tex]
4. Multiply the resultant coefficient by [tex]\(\sqrt{13}\)[/tex]:
[tex]\[
1 \cdot \sqrt{13} = \sqrt{13}
\][/tex]
Thus, the sum of [tex]\(-3 y \sqrt{13}\)[/tex] and [tex]\(4 y \sqrt{13}\)[/tex] is:
[tex]\[
\sqrt{13}
\][/tex]
The numerical value of [tex]\(\sqrt{13}\)[/tex] is approximately:
[tex]\[
\sqrt{13} \approx 3.605551275463989
\][/tex]
So, the combined expression simplifies to:
[tex]\[
y \cdot 3.605551275463989
\][/tex]
Therefore, the sum is:
[tex]\[
y \sqrt{13} \approx y \cdot 3.605551275463989
\][/tex]
