Sure! Let's find the sum of the given terms step-by-step.
Given the terms:
[tex]\[ 4\sqrt{5} \][/tex]
[tex]\[ 2\sqrt{5} \][/tex]
First, we express these terms as:
[tex]\[ \text{Term 1: } 4\sqrt{5} \][/tex]
[tex]\[ \text{Term 2: } 2\sqrt{5} \][/tex]
To find the sum of these terms, we combine them:
[tex]\[ 4\sqrt{5} + 2\sqrt{5} \][/tex]
Since [tex]\(\sqrt{5}\)[/tex] is a common factor in both terms, we can add their coefficients (the numbers in front of the square roots):
[tex]\[ 4\sqrt{5} + 2\sqrt{5} = (4 + 2)\sqrt{5} \][/tex]
Adding the coefficients:
[tex]\[ 4 + 2 = 6 \][/tex]
Thus, the simplified sum is:
[tex]\[ 6\sqrt{5} \][/tex]
Now, let's look at the options provided:
1. [tex]\(6\sqrt{10}\)[/tex]
2. [tex]\(8\sqrt{10}\)[/tex]
3. [tex]\(6\sqrt{5}\)[/tex]
4. [tex]\(8\sqrt{5}\)[/tex]
The correct option that matches our simplified sum [tex]\(6\sqrt{5}\)[/tex] is option 3.
So, the answer is:
[tex]\[ \boxed{3} \][/tex]
