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To find where \(\sqrt{11}\) lies on the number line, we need to approximate its value.

\[
\sqrt{11} \approx 3.3166
\]

Now let's compare this with the given options:

- **Option A: 3 and 4** — \(\sqrt{11}\) is approximately 3.3166, which lies between 3 and 4.
- **Option B: 5 and 6** — This is incorrect, as 3.3166 is not between 5 and 6.
- **Option C: 10 and 11** — Incorrect, since 3.3166 is far less than 10.
- **Option D: 4 and 5** — Incorrect, as \(\sqrt{11}\) is less than 4.

The correct answer is **A: 3 and 4**.

Would you like more details or have any further questions? 

Here are 5 related questions to deepen understanding:

1. What is the square root of 12, and between which two numbers does it lie?
2. How can you estimate square roots of non-perfect squares without a calculator?
3. What is the process of squaring a number and finding its square root?
4. Which two consecutive whole numbers does \(\sqrt{15}\) lie between?
5. How can you visualize square roots on a number line?

**Tip:** When estimating square roots, remember that the square root of a number is between the square roots of the closest perfect squares.

Between which two numbers does √11 lie on a number line?

Understand where the square root of 11 lies on a number line. This problem helps you estimate the square root of non-perfect squares and compare values between whole numbers, suitable for students in Grades 6-8.

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