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To find which two integers \(\sqrt{79}\) is between, we need to determine the two consecutive integers such that the square of the smaller integer is less than 79, and the square of the larger integer is greater than 79.

Let's find the square roots of some integers close to 79:

\[
\sqrt{64} = 8 \quad \text{(since \(64 = 8^2\))}
\]

\[
\sqrt{81} = 9 \quad \text{(since \(81 = 9^2\))}
\]

Since \(64 < 79 < 81\), \(\sqrt{79}\) must be between 8 and 9.

Thus, the correct answer is "8 and 9."

Would you like further details or have any questions? Here are five related questions:

1. What are the steps to approximate the square root of a non-perfect square?
2. How do you determine the square roots of perfect squares?
3. Can you explain the process of finding consecutive integers for other square roots, such as \(\sqrt{50}\)?
4. What is the significance of knowing the square roots of numbers in mathematics?
5. How can understanding square roots help in solving quadratic equations?

**Tip:** When approximating square roots, knowing the squares of numbers around your target can greatly simplify the process.

Learn how to determine which two consecutive integers the square root of 79 lies between by using the properties of square roots. This problem uses basic number theory and square root concepts. Suitable for students in Grades 6-8.

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