To find an equivalent expression for [tex]\(\frac{4}{\sqrt{2}}\)[/tex], we need to rationalize the denominator. Here are the steps to do that:
1. Write the original expression:
[tex]\[
\frac{4}{\sqrt{2}}
\][/tex]
2. Rationalize the denominator:
To eliminate the square root in the denominator, multiply both the numerator and the denominator by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
\frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}
\][/tex]
3. Simplify the expression:
[tex]\[
\frac{4 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{4 \sqrt{2}}{2}
\][/tex]
Since [tex]\(\sqrt{2} \cdot \sqrt{2} = 2\)[/tex], the denominator simplifies to 2.
4. Further simplify the fraction:
Divide the numerator by the denominator:
[tex]\[
\frac{4 \sqrt{2}}{2} = 2 \sqrt{2}
\][/tex]
So, the equivalent expression is [tex]\(\boxed{2 \sqrt{2}}\)[/tex].
Thus, the correct answer is (E) [tex]\(2 \sqrt{2}\)[/tex].
