To determine which two integers $\sqrt{27}$ lies between, we can first approximate the value of $\sqrt{27}$.

We know: $\sqrt{25} = 5 \quad \text{and} \quad \sqrt{36} = 6.$

Since $27$ is between 25 and 36, $\sqrt{27}$ must be between 5 and 6. Therefore, the two integers that $\sqrt{27}$ is between are 5 and 6.

Do you want more details or have any other questions?

Here are 5 related questions:

1. What is $\sqrt{28}$ between?
2. Can you calculate the approximate decimal value of $\sqrt{27}$?
3. What is the square root of a perfect square like 49?
4. How do we find the square root of non-perfect squares?
5. Why is $\sqrt{30}$ closer to 5 than 6?

Tip: When estimating square roots, it's useful to know perfect squares near the number you are working with (e.g., 25, 36).