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The problem presented asks if the expression \( \sqrt[4]{4a^2} \) is equivalent to \( \sqrt{2a} \).

### Step-by-Step Solution:

1. **Simplify \( \sqrt[4]{4a^2} \)**:
   - The fourth root of a product can be broken down: 
   \[
   \sqrt[4]{4a^2} = \sqrt[4]{4} \times \sqrt[4]{a^2}
   \]
   
2. **Simplify each part**:
   - \( \sqrt[4]{4} \) is the same as \( 4^{1/4} \). Since \( 4 = 2^2 \), we have:
     \[
     4^{1/4} = \left(2^2\right)^{1/4} = 2^{1/2} = \sqrt{2}
     \]
   
   - \( \sqrt[4]{a^2} = a^{2/4} = a^{1/2} = \sqrt{a} \).

3. **Combine the simplified results**:
   \[
   \sqrt[4]{4a^2} = \sqrt{2} \times \sqrt{a} = \sqrt{2a}
   \]

Thus, the expression \( \sqrt[4]{4a^2} \) **is indeed equivalent** to \( \sqrt{2a} \).

### Answer:
The correct answer is **"Verdadero"** (True).

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Would you like further details or have any questions?

Here are five related questions to expand on this:
1. How would you simplify \( \sqrt[3]{8a^3} \)?
2. What is the general rule for simplifying roots of products?
3. How does fractional exponentiation relate to roots?
4. Can you explain how \( \sqrt[6]{64a^3} \) would be simplified?
5. What is the difference between a square root and a fourth root in terms of exponents?

**Tip:** Always remember that the \( n \)-th root of a product can be simplified by taking the \( n \)-th root of each factor individually.

¿La expresión \( \sqrt[4]{4a^2} \) es equivalente a \( \sqrt{2a} \)?

Discover how to simplify the radical expression \( \sqrt[4]{4a^2} \) and verify its equivalence to \( \sqrt{2a} \). This problem explains key concepts like the laws of exponents and properties of roots, suitable for students in Grades 9-11.

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