The equation given is:

\[
8 = \sqrt{x^2}
\]

The square root of \(x^2\) is simply the absolute value of \(x\), which we write as:

\[
8 = |x|
\]

This means that \(x\) can either be positive 8 or negative 8:

\[
x = 8 \quad \text{or} \quad x = -8
\]

Therefore, the two possible solutions are:

\[
x = 8 \quad \text{or} \quad x = -8
\]

Would you like more details or have any questions?

Here are five related questions to expand on this concept:

1. What happens if we change the equation to \(9 = \sqrt{x^2}\)?
2. How do you solve \( \sqrt{x^2 + 4} = 10\)?
3. What is the difference between \(\sqrt{x^2}\) and \(x\)?
4. Can you explain how absolute values affect equations like this?
5. How do you solve quadratic equations with square roots?

**Tip:** Always remember that \( \sqrt{x^2} = |x| \), not just \(

Explore how to solve the equation 8 = square root of x^2 using absolute value concepts. This step-by-step guide explains why the square root of x^2 results in |x|, leading to the solutions x = 8 and x = -8. Ideal for students in Grades 6-8.

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