The problem asks to estimate the square root of 78 by identifying two integers that the square root of 78 lies between.

We know the square roots of nearby perfect squares:

• $\sqrt{64} = 8$
• $\sqrt{81} = 9$

Thus, the value of $\sqrt{78}$ lies between 8 and 9. The correct answer would be:

$8 < \sqrt{78} < 9$

Would you like further details, or have any other questions about this?

Here are five related questions:

1. How would you estimate $\sqrt{50}$?
2. What is the square root of a non-perfect square like 72?
3. How do you find the square root of large numbers?
4. Why is estimating square roots important in math?
5. Can you find square roots without a calculator?

Tip: Estimating square roots by knowing nearby perfect squares is a quick mental math trick to approximate answers!