To determine between which two consecutive whole numbers $\sqrt{37}$ lies, let's consider the following:

1. The square root of $36$ is $6$ ($6^2 = 36$).
2. The square root of $49$ is $7$ ($7^2 = 49$).

Thus, $\sqrt{37}$ must lie between $6$ and $7$, because $37$ is greater than $36$ and less than $49$.

Approximation:

We know $\sqrt{37} \approx 6.08$ (since $6.08^2 \approx 37$). Therefore, $\sqrt{37}$ is slightly greater than $6$ but not close to $7$.

Sentence Completion:

Since $\sqrt{36} = 6$ and $\sqrt{49} = 7$, it is known that $\sqrt{37}$ is between $6$ and $7$.

Would you like to visualize this on a number line or need further clarification? Here are 5 related questions:

1. What is the method to find an approximate value of $\sqrt{37}$?
2. How do you calculate square roots manually for numbers like $37$?
3. Can you derive a more precise estimate for $\sqrt{37}$ using a calculator?
4. How does $\sqrt{37}$ compare to other nearby square roots like $\sqrt{35}$ or $\sqrt{40}$?
5. Why are square roots of non-perfect squares considered irrational numbers?

Tip: For approximations, remember the relationship between perfect squares on either side of the given number.