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The question is asking you to approximate the square root of 78 using perfect squares. Let's break down the steps:

1. **Identify two perfect squares** between which \(\sqrt{78}\) lies.
   - The perfect squares near 78 are \(64\) (since \( \sqrt{64} = 8\)) and \(81\) (since \( \sqrt{81} = 9\)).
   - So, \( \sqrt{64} < \sqrt{78} < \sqrt{81} \).
   
2. Therefore, \(\sqrt{78}\) is between 8 and 9.

Here is how the blanks should be filled in:
- \(8 < \sqrt{78} < 9\)

To complete the final sentence:
- \(\sqrt{78}\) is between **8** and **9**.

Would you like more details or have any questions about these steps?

Here are five related questions to further your understanding:
1. How would you approximate \(\sqrt{50}\) using perfect squares?
2. What is the process of estimating \(\sqrt{150}\)?
3. Can you find two perfect squares between which \(\sqrt{120}\) lies?
4. How can you get a better approximation of \(\sqrt{78}\) beyond using perfect squares?
5. What are the steps for estimating cube roots similarly to square roots?

**Tip:** When estimating square roots, remember that perfect squares are numbers like 1, 4, 9, 16, 25, etc., and help you approximate values for non-perfect squares.

Learn how to approximate √78 using nearby perfect squares. This method helps students in Grades 6-8 understand how to estimate square roots between two perfect squares. Suitable for beginners learning square root approximations.

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