To solve the problem, we need to determine the approximate value of $\sqrt{14}$ and then find the correct interval from the given options.

Step 1: Estimate $\sqrt{14}$

The square root of 14 is a number between the square roots of 9 and 16 because: $\sqrt{9} = 3 \quad \text{and} \quad \sqrt{16} = 4$ So, $\sqrt{14}$ is between 3 and 4.

Step 2: Refine the Estimate

To get a better estimate, you can calculate or remember that: $\sqrt{14} \approx 3.74$

Step 3: Choose the Correct Interval

Given the options:

1. Between $-4$ and $-5$
2. Between $-2$ and $-3$
3. Between $-3$ and $-4$
4. Between $-1$ and $-2$

Since we need the value of $-\sqrt{14}$, we negate the positive value: $-\sqrt{14} \approx -3.74$ This value falls between $-4$ and $-3$.

Conclusion

The correct answer is the third option: Between $-3$ and $-4$.

Would you like further details on this problem or have any other questions? Here are some related questions you might find interesting:

1. How would you find the exact value of $\sqrt{14}$?
2. What are some methods to estimate square roots of non-perfect squares?
3. Why is the square root of a number always positive in most cases?
4. How does the negative sign in front of a square root affect its value?
5. Can you solve similar problems for other square roots, such as $\sqrt{20}$?

Tip: When estimating square roots, always check which perfect squares the number lies between to narrow down the value.