what is the following sum?\n4\\sqrt{5}+2\\sqrt{5}\n6\\sqrt{10}\n8\\sqrt{10}\n6\\sqrt{5}\n8\\sqrt{5}

Explanation:

Step1: Identify like - terms

The terms $4\sqrt{5}$ and $2\sqrt{5}$ are like - terms since they have the same radical part $\sqrt{5}$.

Step2: Combine like - terms

We use the distributive property $a\sqrt{b}+c\sqrt{b}=(a + c)\sqrt{b}$. Here, $a = 4$, $c = 2$, and $b = 5$. So, $4\sqrt{5}+2\sqrt{5}=(4 + 2)\sqrt{5}$. $(4 + 2)\sqrt{5}=6\sqrt{5}$

Answer:

C. $6\sqrt{5}$