what is the following sum in simplest form?\n$sqrt{8}+3sqrt{2}+sqrt{32}$\n$3sqrt{8}+3sqrt{2}$\n$5sqrt{42}$\n$…

what is the following sum in simplest form?\n$sqrt{8}+3sqrt{2}+sqrt{32}$\n$3sqrt{8}+3sqrt{2}$\n$5sqrt{42}$\n$9sqrt{2}$\n$5sqrt{2}+sqrt{32}$

what is the following sum in simplest form?\n$sqrt{8}+3sqrt{2}+sqrt{32}$\n$3sqrt{8}+3sqrt{2}$\n$5sqrt{42}$\n$9sqrt{2}$\n$5sqrt{2}+sqrt{32}$

Answer

Explanation:

Step1: Simplify each square - root term

Simplify $\sqrt{8}$: $\sqrt{8}=\sqrt{4\times2}=\sqrt{4}\times\sqrt{2}=2\sqrt{2}$; simplify $\sqrt{32}$: $\sqrt{32}=\sqrt{16\times2}=\sqrt{16}\times\sqrt{2}=4\sqrt{2}$.

Step2: Substitute the simplified terms into the original expression

The original expression $\sqrt{8}+3\sqrt{2}+\sqrt{32}$ becomes $2\sqrt{2}+3\sqrt{2}+4\sqrt{2}$.

Step3: Combine like - terms

$(2 + 3+4)\sqrt{2}=9\sqrt{2}$.

Answer:

C. $9\sqrt{2}$