https://file.aiquickdraw.com/mathbot/file/17262502608758x9m1gqf.jpg

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.

Compare -√7 and -3.12345... Justify your reasoning.

Learn how to compare -√7 and -3.12345 with a step-by-step explanation. This problem covers key mathematical concepts like square roots and comparing negative decimal values. Suitable for students in Grades 8-10.

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