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To rationalize the denominator of the given expression:

\[
\frac{4x^2}{\sqrt{5x}}
\]

we need to eliminate the square root from the denominator. This is typically done by multiplying both the numerator and the denominator by the conjugate or an appropriate factor that will clear the square root. 

### Steps to Rationalize:

1. **Identify the denominator:** The denominator is \(\sqrt{5x}\).
2. **Multiply by the appropriate factor:** To eliminate the square root in the denominator, we multiply both the numerator and the denominator by \(\sqrt{5x}\).

\[
\frac{4x^2}{\sqrt{5x}} \times \frac{\sqrt{5x}}{\sqrt{5x}} = \frac{4x^2 \cdot \sqrt{5x}}{5x}
\]

3. **Simplify the expression:** 
   
   - The numerator becomes \(4x^2 \sqrt{5x}\).
   - The denominator simplifies to \(5x\).

Thus, the rationalized form is:

\[
\frac{4x^2 \sqrt{5x}}{5x}
\]

4. **Simplify further if possible:** 

Since there is an \(x\) in both the numerator and the denominator, we can cancel one \(x\):

\[
\frac{4x \sqrt{5x}}{5}
\]

### Final Answer:

The expression with a rationalized denominator is:

\[
\frac{4x \sqrt{5x}}{5}
\]

Would you like further details, or do you have any questions?

### Related Questions:

1. How do you rationalize the denominator if it contains a binomial with a square root?
2. What is the general method for simplifying square roots in the denominator?
3. How do you multiply and divide expressions with radicals?
4. Can you explain how to simplify higher-order roots in a denominator?
5. What happens when you have a square root in both the numerator and the denominator?

### Tip:

When rationalizing denominators with radicals, always look for the simplest way to remove the radical by multiplying by its conjugate or an appropriate factor.

Rationalize the denominator for the expression 4x^2 / √(5x).

Learn how to rationalize the denominator of the expression 4x^2 / √(5x) by eliminating the square root. This problem involves algebraic concepts like simplifying radicals and fractions, suitable for students in Grades 9-10.

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