The given problem is to simplify $\frac{4}{\sqrt{2}}$ and match it to one of the multiple-choice answers.

Solution:

To simplify $\frac{4}{\sqrt{2}}$, we follow these steps:

1. Rationalize the denominator:
   Multiply both the numerator and denominator by $\sqrt{2}$: $\frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{4\sqrt{2}}{2}.$

2. Simplify the fraction:
   Divide $4\sqrt{2}$ by $2$: $\frac{4\sqrt{2}}{2} = 2\sqrt{2}.$

Thus, the simplified form is $2\sqrt{2}$.

Final Answer:

The correct choice is A) $2\sqrt{2}$.

Would you like further details about rationalization or simplifying radicals?

5 Related Questions:

1. How do you simplify other expressions with square roots in the denominator, such as $\frac{5}{\sqrt{3}}$?
2. What does "rationalizing the denominator" mean, and why is it important?
3. How would $\frac{4}{\sqrt{3}}$ simplify?
4. What are the properties of square roots used in simplification?
5. Can the expression $\frac{4}{\sqrt{2}}$ be simplified in a different way?

Tip:

Always rationalize the denominator to ensure the result is in standard form!