To determine between which two numbers $\sqrt{374}$ lies, we can check the squares of the numbers given:

$19^2 = 361$ $20^2 = 400$

Since $374$ lies between $361$ and $400$, $\sqrt{374}$ must lie between 19 and 20.

So, $\sqrt{374}$ is between 19 and 20.

Would you like more details or have any questions about this?

Here are five related questions:

1. What is $\sqrt{375}$ approximately?
2. How do we estimate square roots of non-perfect squares?
3. What is $\sqrt{361}$ and $\sqrt{400}$?
4. How do you solve for square roots using long division?
5. How can you calculate cube roots?

Tip: Estimating square roots of non-perfect squares can be done by finding the closest perfect squares and narrowing down from there!