Let's break down each step to solve the given sum: [tex]\( 4 \sqrt{5} + 2 \sqrt{5} \)[/tex].
1. Identify like terms: In this expression, [tex]\( 4 \sqrt{5} \)[/tex] and [tex]\( 2 \sqrt{5} \)[/tex] are like terms because they both contain the same radical part [tex]\( \sqrt{5} \)[/tex].
2. Add the coefficients: To add like terms, we simply need to add their coefficients. The coefficients of [tex]\( 4 \sqrt{5} \)[/tex] and [tex]\( 2 \sqrt{5} \)[/tex] are 4 and 2, respectively.
[tex]\[
4 \sqrt{5} + 2 \sqrt{5} = (4 + 2) \sqrt{5}
\][/tex]
3. Simplify the expression: Now, we add the coefficients together:
[tex]\[
4 + 2 = 6
\][/tex]
Therefore, we get:
[tex]\[
(4 + 2) \sqrt{5} = 6 \sqrt{5}
\][/tex]
We get that the solution simplifies to [tex]\( 6 \sqrt{5} \)[/tex], which equals approximately 13.416407864998739.
Based on this calculation, the correct answer from the given options is:
[tex]\[
6 \sqrt{5}
\][/tex]
