In the given image, the task is to compare $-\sqrt{7}$ and approximately -3.12345. The goal is to determine whether $-3.12345$ is greater than, less than, or equal to $-\sqrt{7}$.

Step-by-step solution:

1. Calculate $\sqrt{7}$: $\sqrt{7} \approx 2.64575$

2. Negate the square root: $-\sqrt{7} \approx -2.64575$

3. Compare the two values:

   • We are comparing $-3.12345$ with $-2.64575$.
   • Since $-3.12345$ is more negative than $-2.64575$, we have: $-3.12345 < -\sqrt{7}$

Conclusion:

$-3.12345 < -\sqrt{7}$ Thus, the correct symbol to choose is $<$.

Would you like further details or have any questions?

Here are five related questions:

1. How do you approximate square roots without a calculator?
2. What is the difference between comparing negative and positive numbers?
3. Can you compare other roots like $\sqrt{5}$ and decimals?
4. What happens when you compare fractions and square roots?
5. How can you simplify expressions involving square roots?

Tip: When comparing two negative numbers, the one with the larger absolute value is always the smaller number.