`(6.5)^(2)=?`

Options

A. 58
B. 25
C. 43
D. 35

Explanation

To find the value of \( (6.5)^2 \) using approximation, we can follow these steps:

### Step 1: Identify the perfect squares around 6.5
First, we need to find the perfect squares of the whole numbers that are closest to 6.5. The two whole numbers we will consider are 6 and 7.

- \( 6^2 = 36 \)
- \( 7^2 = 49 \)

### Step 2: Establish the range
Since \( 6.5 \) is between \( 6 \) and \( 7 \), we know that:

\[ 36 < (6.5)^2 < 49 \]

### Step 3: Calculate the midpoint
To get a better approximation, we can calculate the average of \( 36 \) and \( 49 \):

\[ \text{Midpoint} = \frac{36 + 49}{2} = \frac{85}{2} = 42.5 \]

This tells us that \( (6.5)^2 \) is likely to be around \( 42.5 \).

### Step 4: Evaluate the options
Now, we can evaluate the options based on our approximation. We know:

- \( 36 < (6.5)^2 < 49 \)
- Our midpoint approximation is \( 42.5 \)

Assuming the options are: 25, 35, 43, and 58.

- **25** is less than \( 36 \) (not possible).
- **35** is also less than \( 36 \) (not possible).
- **58** is greater than \( 49 \) (not possible).
- **43** is between \( 36 \) and \( 49 \), and it is close to our midpoint of \( 42.5 \).

### Conclusion
Therefore, the most reasonable approximation for \( (6.5)^2 \) is:

\[ (6.5)^2 \approx 43 \]

### Final Answer
Thus, \( (6.5)^2 = 43 \).

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