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Let's solve the expressions in Column A by simplifying the radicals and then matching them with the choices in Column B.

### 1. \(\sqrt[4]{54}\)

We cannot simplify 54 to have any perfect fourth powers as factors. So this expression remains as is, which means it matches:
- **F. \( 3 \sqrt[3]{2} \)**.

### 2. \(\sqrt[4]{625x^8}\)

\(625 = 5^4\), and the exponent on \(x\) is 8, which means it can be simplified:
\[
\sqrt[4]{625x^8} = 5x^2
\]
Thus, this matches:
- **G. \( 5x^2 \)**.

### 3. \(\sqrt{\frac{25x^3}{100x^2}}\)

First, simplify the fraction inside the radical:
\[
\frac{25x^3}{100x^2} = \frac{1}{4}x
\]
Now take the square root:
\[
\sqrt{\frac{1}{4}x} = \frac{1}{2}x^{1/2} = \frac{x}{2}
\]
This matches:
- **D. \( \frac{x}{2} \)**.

### 4. \(\sqrt{81x^4y^2}\)

First, simplify inside the square root:
\[
\sqrt{81x^4y^2} = 9x^2y
\]
This matches:
- **C. \( 9x^2y \)**.

### 5. \(\sqrt{300x^5y^3}\)

Factor 300 as \(300 = 100 \times 3 = 10^2 \times 3\). Now simplify:
\[
\sqrt{300x^5y^3} = 10x^2y \sqrt{3xy}
\]
This matches:
- **E. \( 10x^2y \sqrt{3xy} \)**.

### Final Answer:
1. F  
2. G  
3. D  
4. C  
5. E

Would you like more detailed steps or any specific clarifications?

Here are 5 related questions to explore further:
1. How do you simplify radicals involving variables with even and odd exponents?
2. What are the general rules for simplifying higher roots like cube roots and fourth roots?
3. How do you approach simplifying fractional radicals?
4. How do you factor numbers to simplify square roots quickly?
5. What happens if there are negative numbers inside even roots?

**Tip:** Always check if the number inside a root can be factored to include perfect squares, cubes, etc., to simplify the expression easily.

Simplify the following expressions by reducing the radicand as much as possible. Match the expressions in column A with the correct simplified form in column B.

This exercise focuses on simplifying radicals and matching the expressions with their correct simplified forms. Explore how to handle fourth roots, square roots, and algebraic expressions with variables and coefficients. Suitable for students in Grades 9-10.

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