To simplify the expression [tex]\(5 \sqrt{8} - \sqrt{18} - 2 \sqrt{2}\)[/tex], let's first break down each term individually and then combine them step-by-step.
1. Simplify [tex]\(5 \sqrt{8}\)[/tex]:
[tex]\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2 \sqrt{2}
\][/tex]
So:
[tex]\[
5 \sqrt{8} = 5 \cdot 2 \sqrt{2} = 10 \sqrt{2}
\][/tex]
2. Simplify [tex]\(\sqrt{18}\)[/tex]:
[tex]\[
\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3 \sqrt{2}
\][/tex]
3. Consider [tex]\(2 \sqrt{2}\)[/tex], which is already in simplified form.
Now, combining all simplified terms:
[tex]\[
5 \sqrt{8} - \sqrt{18} - 2 \sqrt{2} = 10 \sqrt{2} - 3 \sqrt{2} - 2 \sqrt{2}
\][/tex]
Add up the coefficients of [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
(10 - 3 - 2) \sqrt{2} = 5 \sqrt{2}
\][/tex]
Thus, the simplified form of the given expression is:
[tex]\[
5 \sqrt{2}
\][/tex]
So the correct simplified form is:
[tex]\[
\boxed{5 \sqrt{2}}
\][/tex]
