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To solve the problem, we need to simplify the expression:  
\[
-\sqrt{\frac{64}{36}}
\]

### Step 1: Simplify the Square Root of the Fraction
The square root of a fraction can be taken by separately taking the square root of the numerator and the denominator. So, we have:
\[
-\sqrt{\frac{64}{36}} = -\frac{\sqrt{64}}{\sqrt{36}}
\]

### Step 2: Evaluate the Square Roots
- The square root of 64 is 8, since \(8 \times 8 = 64\).
- The square root of 36 is 6, since \(6 \times 6 = 36\).

This gives us:
\[
-\frac{\sqrt{64}}{\sqrt{36}} = -\frac{8}{6}
\]

### Step 3: Simplify the Fraction
Now, simplify \(-\frac{8}{6}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[
-\frac{8}{6} = -\frac{4}{3}
\]

### Final Answer
The answer is:
\[
-\frac{4}{3}
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the square root of a fraction where both the numerator and the denominator are perfect squares?
2. How do you convert an improper fraction to a mixed number?
3. What are the rules for simplifying negative square roots?
4. How can we simplify square roots of non-perfect squares?
5. Why do we sometimes take the negative of a square root?

### Tip:
To simplify square roots of fractions, always check if both the numerator and denominator are perfect squares for easy simplification.

Learn how to simplify -√(64/36) by taking the square roots of both the numerator and the denominator separately. This math problem involves concepts like square roots, negative values, and fraction simplification, making it ideal for Grade 8 students.

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