`(14.5)^(2)=?`

Options

A. 235
B. 190
C. 250
D. 210

Explanation

To find the square of \( 14.5 \) using approximation, we can follow these steps:

### Step 1: Identify the perfect squares around \( 14.5 \)
We know that:
- \( 14^2 = 196 \)
- \( 15^2 = 225 \)

### Step 2: Understand the position of \( 14.5 \)
The number \( 14.5 \) is exactly halfway between \( 14 \) and \( 15 \). Therefore, its square will be between \( 196 \) and \( 225 \).

### Step 3: Estimate the square of \( 14.5 \)
Since \( 14.5 \) is halfway between \( 14 \) and \( 15 \), we can estimate that its square will be closer to the average of \( 196 \) and \( 225 \).

### Step 4: Calculate the average of \( 196 \) and \( 225 \)
To find the average:
\[ \text{Average} = \frac{196 + 225}{2} = \frac{421}{2} = 210.5 \]

### Step 5: Conclusion
Since \( 14.5^2 \) is approximately \( 210.5 \), we can round it to \( 210 \) for practical purposes. Thus, we conclude that:
\[ (14.5)^2 \approx 210 \]

### Final Answer
The approximate value of \( (14.5)^2 \) is \( 210 \).

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