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To find the domain of the expression \( \sqrt{5x - 2} \), we need to ensure that the expression inside the square root is non-negative, as the square root of a negative number is not defined within the real numbers.

### Steps to Determine the Domain:
1. Set up the inequality:  
   \[
   5x - 2 \geq 0
   \]

2. Solve for \( x \):
   \[
   5x \geq 2
   \]
   \[
   x \geq \frac{2}{5}
   \]

### Conclusion:
The domain of the expression \( \sqrt{5x - 2} \) is:
\[
x \geq \frac{2}{5}
\]
or, in interval notation, \(\left[ \frac{2}{5}, \infty \right)\).

Would you like more details, or have any questions on this solution?

### Related Questions:
1. How would the domain change if the expression were \( \sqrt{7x + 3} \)?
2. What would be the domain if the square root were replaced with a cube root, such as \( \sqrt[3]{5x - 2} \)?
3. How does adding an additional term outside the square root, like \( \sqrt{5x - 2} + 3 \), affect the domain?
4. What is the domain of \( \frac{1}{\sqrt{5x - 2}} \)?
5. How does the concept of domain apply to functions with multiple variables, like \( \sqrt{5x - 2y} \)?

### Tip:
When determining the domain of a square root expression, always look for values that keep the radicand (the expression inside the square root) non-negative.

Learn how to find the domain of the square root function \( \sqrt{5x - 2} \) by ensuring the expression inside the root is non-negative. This problem covers key algebra concepts related to function domains and square root functions, suitable for Grades 8-10.

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