Solve by using the square root property. Express the solution set in exact simplest form:
(w+6)^2 = 40

To solve the equation \((w + 6)^2 = 40\) using the square root property, follow these steps:

1. **Apply the square root property**:
   \[
   w + 6 = \pm \sqrt{40}
   \]

2. **Simplify the square root**:
   \[
   \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}
   \]
   So, the equation becomes:
   \[
   w + 6 = \pm 2\sqrt{10}
   \]

3. **Solve for \( w \)**:
   \[
   w = -6 \pm 2\sqrt{10}
   \]

Thus, the solution set is:
\[
w = -6 + 2\sqrt{10} \quad \text{or} \quad w = -6 - 2\sqrt{10}
\]

The exact simplest form of the solution set is:
\[
\boxed{-6 + 2\sqrt{10},\ -6 - 2\sqrt{10}}
\]

Would you like any details or have any questions? Here are some related problems to try:

1. Solve \((x - 5)^2 = 25\) using the square root property.
2. Solve \( (y + 3)^2 = 18 \) using the square root property.
3. Solve \((z + 4)^2 = 72\) and express the solution in simplest form.
4. Solve \((k - 2)^2 = 50\) and simplify your answer.
5. Solve \( (m + 7)^2 = 12 \) using the square root property.

**Tip:** Always remember to consider both the positive and negative roots when applying the square root property.

Learn how to solve the equation (w + 6)^2 = 40 using the square root property with a step-by-step explanation. This problem covers algebraic concepts including the square root property and provides an exact simplest form solution set. Suitable for advanced high school students.

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