The expression given is \(\sqrt{x^2} - 5 + 4\).

### Simplifying the Expression:

1. **Square Root of \(x^2\):**
   \[
   \sqrt{x^2} = |x|
   \]
   Here, the square root of \(x^2\) is the absolute value of \(x\), denoted as \(|x|\).

2. **Simplify further:**
   \[
   |x| - 5 + 4
   \]
   Combine the constants:
   \[
   |x| - 1
   \]

### Final Expression:
The simplified expression is \(|x| - 1\).

### Summary:
The expression simplifies to \(|x| - 1\), where \(|x|\) represents the absolute value of \(x\). This means the expression is always non-negative, except when \(x = 0\), where the value is \(-1\).

Would you like any further details or have any questions?

### Related Questions:
1. What is the domain and range of \(|x| - 1\)?
2. How do you graph \(|x| - 1\)?
3. What is the minimum value of \(|x| - 1\)?
4. How does \(|x| - 1\) compare to \(|x|\)?
5. Can \(|x| - 1\) equal zero? If so, for what value of \(x\)?

**Tip:** The absolute value function \(|x|\) is always non-negative and represents the distance of \(x\) from zero on the number line.

Learn how to simplify the expression √x² - 5 + 4 step-by-step. Understand the concepts of square root and absolute value in algebra. Suitable for high school students.

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