Let's estimate the value of the expression given:

$\frac{6.21^2}{3.74}$

To simplify this, we round the numbers for an easier approximation.

1. Round 6.21 to 6.
2. Round 3.74 to 4.

So, we now estimate:

$\frac{6^2}{4} = \frac{36}{4} = 9$

Thus, the estimated value of the expression is 9.

Would you like a more detailed explanation or further assistance? Here are some related questions for you:

1. How can you improve your estimation using different rounding strategies?
2. What other methods can be used to estimate values for complex expressions?
3. How do you decide which numbers to round when estimating in math problems?
4. What is the importance of rounding in everyday life?
5. How does estimation help in problem-solving, especially in practical scenarios?

Tip: Estimating is useful in quick problem-solving when exact answers are not necessary. It can help check the reasonableness of your calculations.