Which of the following integers is closest to `(sqrt50)/(2)`?

Options

A. 3
B. 4
C. 5
D. 13

Answer

To find which integer is closest to \(\frac{\sqrt{50}}{2}\), we can follow these steps:

### Step 1: Calculate \(\sqrt{50}\)
We know that:
\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

### Step 2: Approximate \(\sqrt{2}\)
The approximate value of \(\sqrt{2}\) is about \(1.414\). Therefore:
\[ \sqrt{50} \approx 5 \times 1.414 = 7.07 \]

### Step 3: Divide by 2
Now, we divide this approximate value by 2:
\[ \frac{\sqrt{50}}{2} \approx \frac{7.07}{2} \approx 3.535 \]

### Step 4: Identify the Closest Integer
Next, we need to determine which integer is closest to \(3.535\). The integers around \(3.535\) are \(3\) and \(4\).

### Step 5: Compare Distances
- The distance from \(3.535\) to \(3\) is:
\[ 3.535 - 3 = 0.535 \]
- The distance from \(3.535\) to \(4\) is:
\[ 4 - 3.535 = 0.465 \]

Since \(0.465 < 0.535\), \(3.535\) is closer to \(4\) than to \(3\).

### Conclusion
Thus, the integer closest to \(\frac{\sqrt{50}}{2}\) is \(4\).

### Answer
The closest integer to \(\frac{\sqrt{50}}{2}\) is \(4\).

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