To solve the problem, we need to evaluate the sum [tex]\(4 \sqrt{5} + 2 \sqrt{5}\)[/tex].
Let's break it down step-by-step:
1. First, evaluate the term [tex]\(4 \sqrt{5}\)[/tex]. This means we are multiplying 4 by the square root of 5. Numerically, this is:
[tex]\[
4 \sqrt{5} \approx 8.94427190999916
\][/tex]
2. Next, evaluate the term [tex]\(2 \sqrt{5}\)[/tex]. This means we are multiplying 2 by the square root of 5. Numerically, this is:
[tex]\[
2 \sqrt{5} \approx 4.47213595499958
\][/tex]
3. Now, we sum the two results:
[tex]\[
4 \sqrt{5} + 2 \sqrt{5} = 8.94427190999916 + 4.47213595499958 \approx 13.416407864998739
\][/tex]
Thus, [tex]\(4 \sqrt{5} + 2 \sqrt{5}\)[/tex] simplifies to:
[tex]\[
6 \sqrt{5}
\][/tex]
So, the correct answer to the question is [tex]\(6 \sqrt{5}\)[/tex].
