To solve the expression [tex]\(\sqrt{8} + 2\sqrt{32} - \sqrt{2}\)[/tex], let's break it down step-by-step and simplify each term:
1. Simplifying [tex]\(\sqrt{8}\)[/tex]:
[tex]\[
\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
\][/tex]
2. Simplifying [tex]\(2\sqrt{32}\)[/tex]:
[tex]\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}
\][/tex]
[tex]\[
2\sqrt{32} = 2 \times 4\sqrt{2} = 8\sqrt{2}
\][/tex]
3. [tex]\(\sqrt{2}\)[/tex] is already in its simplest form.
Now, we combine the simplified terms:
[tex]\[
2\sqrt{2} + 8\sqrt{2} - \sqrt{2}
\][/tex]
Combine like terms:
[tex]\[
(2 + 8 - 1)\sqrt{2}
\][/tex]
[tex]\[
9\sqrt{2}
\][/tex]
So, the simplified form of the expression is:
[tex]\[
\sqrt{8} + 2\sqrt{32} - \sqrt{2} = 9\sqrt{2}
\][/tex]
Thus, the correct answer is:
D) [tex]\(9\sqrt{2}\)[/tex]
