To solve or simplify the expression \( \sqrt{x^2 - 9x} \), there are a few possible approaches depending on what you're looking for.

### Case 1: Simplification
We start with the expression:
\[
\sqrt{x^2 - 9x}
\]
This is already in its simplest form. There's no further simplification unless we factor the quadratic expression inside the square root.

Factoring \( x^2 - 9x \):
\[
x^2 - 9x = x(x - 9)
\]
So, the expression becomes:
\[
\sqrt{x(x - 9)}
\]

### Case 2: Solving the Equation (if you meant \( \sqrt{x^2 - 9x} = 0 \))
If you want to solve for \( x \) where the expression equals zero, set:
\[
\sqrt{x^2 - 9x} = 0
\]
Square both sides:
\[
x^2 - 9x = 0
\]
Factor the quadratic:
\[
x(x - 9) = 0
\]
Thus, \( x = 0 \) or \( x = 9 \).

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

### Related Questions:
1. What is the domain of \( \sqrt{x^2 - 9x} \)?
2. How would you solve \( \sqrt{x^2 - 9x} = 5 \)?
3. What does the graph of \( \sqrt{x^2 - 9x} \) look like?
4. Can we simplify the expression if we know more about the values of \( x \)?
5. How would we compute the derivative of \( \sqrt{x^2 - 9x} \)?

### Tip:
Always ensure the expression inside a square root is non-negative to avoid complex numbers when working in real-number contexts.

The query submitted by the user: \sqrt{x^{2}-9x}

Explore how to simplify and solve the expression \sqrt{x^{2}-9x}. This problem includes key algebraic concepts like factoring quadratics and applying the zero-product property. Suitable for students in Grades 8-10.

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