https://file.aiquickdraw.com/mathbot/file/1730072464540tquc1sgk.jpg

The problem presented is:

\[
36k^2 = 25
\]

Let's solve for \( k \):

1. **Isolate \( k^2 \):**
   \[
   k^2 = \frac{25}{36}
   \]

2. **Take the square root of both sides:**
   \[
   k = \pm \sqrt{\frac{25}{36}}
   \]

3. **Simplify the square root:**
   \[
   k = \pm \frac{\sqrt{25}}{\sqrt{36}} = \pm \frac{5}{6}
   \]

Therefore, the solutions for \( k \) are \( k = \frac{5}{6} \) and \( k = -\frac{5}{6} \).

### Answer
The correct answer is **D. \( \frac{5}{6}, -\frac{5}{6} \)**.

Would you like a detailed explanation on any step or have more questions? 

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Here are some related questions to explore:

1. How do we determine if a square root should include a positive and negative solution?
2. Why do we divide both sides by 36 to isolate \( k^2 \)?
3. How does simplifying square roots work in fractional form?
4. What would happen if we had a negative number on the right side of the equation?
5. How can we check if our solutions for \( k \) are correct?

**Tip:** When solving equations, always ensure the variable you’re solving for is isolated before taking any square roots or other operations.

Learn how to solve the equation 36k² = 25 by isolating the variable and using square roots. This algebraic problem emphasizes the concept of quadratic solutions, including both positive and negative roots. Suitable for students in Grades 8-10.

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