To calculate $\sqrt{424}$, you can follow these steps:

1. Estimate the Range:

   • Find two perfect squares between which 424 lies.
   • $20^2 = 400$ and $21^2 = 441$, so $\sqrt{424}$ is between 20 and 21.

2. Use Approximation:

   • You can start with a rough estimate, say, 20.5, and square it: $20.5^2 = 420.25$
   • Since $420.25$ is close to $424$, but less, the square root must be slightly more than 20.5.

3. Refine the Approximation:

   • Try a value like 20.6: $20.6^2 = 424.36$
   • This is very close to 424. Hence, $\sqrt{424} \approx 20.6$.

4. Exact Calculation:

   • For more precision, use a calculator to find: $\sqrt{424} \approx 20.59126$
   • This value can be rounded depending on the required precision.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you calculate square roots by hand using the long division method?
2. What are some common methods for approximating square roots without a calculator?
3. How can you estimate square roots using linear interpolation?
4. Why is the square root of a non-perfect square always an irrational number?
5. What are the applications of square roots in real-life problems?

Tip: When approximating square roots, always check how close your squared value is to the original number to refine your estimate further.