https://file.aiquickdraw.com/mathbot/file/172670992785574o3nx1s.jpg

The expression in the image is:

\[
\sqrt{x^2 - 6x + 9}
\]

To simplify this expression, we first notice that the quadratic expression inside the square root can be factored. The expression \(x^2 - 6x + 9\) is a perfect square trinomial, which factors as:

\[
x^2 - 6x + 9 = (x - 3)^2
\]

Thus, the expression simplifies to:

\[
\sqrt{(x - 3)^2} = |x - 3|
\]

The absolute value is needed because the square root of a square always yields the non-negative result.

Therefore, the simplified form of the expression is:

\[
|x - 3|
\]

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you determine if a quadratic expression is a perfect square?
2. What are the steps to factor a quadratic trinomial?
3. Why is the absolute value needed after simplifying a square root of a squared term?
4. How would this expression change if it was under a cube root instead of a square root?
5. What happens to this expression when you substitute specific values of \(x\)?

**Tip**: Always check for perfect square trinomials when simplifying expressions under a square root, as they lead to clean simplifications.

Simplify the expression √(x^2 - 6x + 9).

This solution simplifies the expression √(x^2 - 6x + 9) by factoring the quadratic into a perfect square trinomial, then applying square root rules. Learn how to simplify such expressions, suitable for Grades 8-10.

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