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.