Let's evaluate the expression:

\[
\sqrt{\left(-7\right)^2}
\]

### Step 1: Evaluate the squared term inside the square root.

\[
(-7)^2 = (-7) \times (-7) = 49
\]

### Step 2: Take the square root of the result.

\[
\sqrt{49} = 7
\]

So, the value of the expression is:

\[
\sqrt{\left(-7\right)^2} = 7
\]

### Explanation
- The squaring operation removes the negative sign, resulting in a positive number.
- Taking the square root of a positive number always yields the positive principal root.

Would you like more details or have any questions?

### Related Questions:
1. What is \(\sqrt{(-x)^2}\) for any value of \(x\)?
2. How does the square root function behave with negative inputs?
3. Why is the principal square root always non-negative?
4. What is \(\sqrt{x^2}\) when \(x\) is negative?
5. How does the absolute value function relate to square roots and squares?

**Tip:** The principal square root of any squared number is always the absolute value of the original number.

Understand how to evaluate the mathematical expression √((-7)^2). Follow a step-by-step explanation to learn about square roots, exponentiation, and handling negative numbers in mathematics. Suitable for students in Grades 7-9.

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