Yes, $\frac{1}{2\sqrt{2}}$ is equal to $\frac{\sqrt{2}}{2}$.

Here’s why:

Starting with $\frac{1}{2\sqrt{2}}$, we can simplify it by rationalizing the denominator.

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

2. This expression is now $\frac{\sqrt{2}}{4}$.

Now, notice that the denominator is $4$ in both cases when we rationalize the denominator, and it's $\frac{\sqrt{2}}{2}$.

Let me know if you'd like a more detailed breakdown! Also, feel free to ask about other related concepts or questions you may have.

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Here are some follow-up questions you might find interesting:

1. What does it mean to "rationalize the denominator"?
2. Can all irrational denominators be simplified using this method?
3. How do you simplify other expressions involving square roots?
4. Why does multiplying by $\sqrt{2}/\sqrt{2}$ help?
5. Are there other methods for simplifying fractions involving square roots?

Tip: Always try to simplify expressions with square roots by rationalizing the denominator when possible, as it helps make calculations easier!