The image shows a table with squares of values and their corresponding square roots, and a question asking which value should be used to find $\sqrt{50}$ using the nearest function.

The table is divided into two sections:

1. First Section:

   • Squares: $5.0^2$, $5.1^2$, $5.2^2$, $5.3^2$, $5.4^2$
   • Values: 25.0, 26.0, 27.0, 28.1, 29.2, 30.3

2. Second Section:

   • Squares: $5.6^2$, $5.7^2$, $5.8^2$, $5.9^2$, $6.0^2$
   • Values: 31.4, 32.5, 33.6, 34.8, 36.0

Analyzing the Table:

To estimate $\sqrt{50}$, look for the square that is closest to 50.

From the given squares:

• $5.6^2 = 31.4$
• $5.7^2 = 32.5$
• $5.8^2 = 33.6$
• $5.9^2 = 34.8$
• $6.0^2 = 36.0$

None of these values in the table reach close to 50 directly, but understanding that $\sqrt{50}$ lies between the squares of 7.0 and 7.1 might lead to the correct choice.

$\sqrt{50}$ is approximately 7.071, which is close to 7.1. So, the square root calculation closest to $7.071$ could be in a square table of squares above $6.0^2$.

Thus, the correct answer would likely use squares of $7.0^2$ or $7.1^2$ to calculate $\sqrt{50}$.

Would you like more details or have any questions? Here are 5 relative questions you might find useful:

1. How do you calculate square roots using interpolation between given squares?
2. What is the significance of choosing a nearby square for estimating square roots?
3. Can you use this method for non-perfect squares, like $\sqrt{55}$?
4. How does the nearest square method compare to using a calculator for square roots?
5. What are other methods to approximate square roots without a calculator?

Tip: Understanding square values and their roots helps in quickly estimating square roots, especially in exams where calculators are not allowed.