Determine which two values the following expression is between 3√7

We are tasked with finding between which two integer values the expression \(3\sqrt{7}\) lies. To solve this, we first approximate the value of \( \sqrt{7} \).

The square root of 7 is approximately:
\[
\sqrt{7} \approx 2.64575
\]

Now, multiply this by 3:
\[
3\sqrt{7} \approx 3 \times 2.64575 = 7.93725
\]

Thus, \( 3\sqrt{7} \) is approximately 7.93725, which means the value lies between 7 and 8.

### Conclusion:
The expression \(3\sqrt{7}\) is between the values **7 and 8**.

Would you like more details on how square roots are approximated, or do you have further questions?

Here are 5 related questions to consider:
1. How do you calculate square roots manually?
2. What is the approximation of \(\sqrt{5}\)?
3. What is the value of \(4\sqrt{10}\)?
4. How can we use inequalities to show bounds of expressions involving square roots?
5. How do irrational numbers like \(\sqrt{7}\) differ from rational numbers?

**Tip:** When approximating square roots, you can always square nearby integers to estimate the closest possible values.

Determine which two values the following expression is between: 3√7.

Find out between which two integer values the expression 3√7 lies. Learn how to approximate square roots and multiply them. This problem involves approximating √7 to 2.64575 and multiplying it by 3 to get 7.93725, making it lie between 7 and 8. Suitable for students in Grades 6-8.

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