Let's solve the equation using the Square Root Property.

Given:
\[
(y + 8)^2 = 12
\]

### Steps to Solve:

1. **Take the square root of both sides:**
   \[
   \sqrt{(y + 8)^2} = \pm \sqrt{12}
   \]
   Simplifying, we get:
   \[
   y + 8 = \pm \sqrt{12}
   \]

2. **Simplify \(\sqrt{12}\):**
   \[
   \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}
   \]
   So the equation becomes:
   \[
   y + 8 = \pm 2\sqrt{3}
   \]

3. **Isolate \(y\) by subtracting 8 from both sides:**
   \[
   y = -8 \pm 2\sqrt{3}
   \]

### Final Answer:

The solutions are:
\[
y = -8 + 2\sqrt{3} \quad \text{or} \quad y = -8 - 2\sqrt{3}
\]

Would you like any further details or have any questions?

### Related Questions:
1. How do you simplify square roots like \(\sqrt{12}\)?
2. Can you solve \( (z - 5)^2 = 20 \) using the Square Root Property?
3. What happens if the square root simplifies to a whole number?
4. How do you check your solutions for equations like this?
5. What other methods can be used to solve quadratic equations?

**Tip:** When dealing with square roots, always factor the number under the square root to its prime factors to simplify it.

Learn how to solve the equation (y + 8)^2 = 12 using the square root property with a detailed step-by-step solution. This problem involves quadratic equations and the application of the square root property in algebra. Suitable for students in Grades 9-12.

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