Which of the following is closest to `sqrt(3)` ?

Options

A. `(9)/(5)`
B. `1.75`
C. `(173)/(100)`
D. `1.69`

Answer

To find which of the given options is closest to \(\sqrt{3}\), we will first determine the approximate value of \(\sqrt{3}\) and then compare it with each of the options provided.

### Step 1: Calculate \(\sqrt{3}\)
The value of \(\sqrt{3}\) is approximately \(1.732\).

### Step 2: Evaluate the Options
Now, we will evaluate each option to see which one is closest to \(1.732\).

1. **Option 1: \(\frac{9}{5}\)**
\[ \frac{9}{5} = 1.8 \]

2. **Option 2: \(1.75\)**
\[ 1.75 \text{ (already in decimal form)} \]

3. **Option 3: \(\frac{173}{100}\)**
\[ \frac{173}{100} = 1.73 \]

4. **Option 4: \(1.69\)**
\[ 1.69 \text{ (already in decimal form)} \]

### Step 3: Compare the Values
Now we compare the calculated values with \(1.732\):

- \(|1.8 - 1.732| = 0.068\)
- \(|1.75 - 1.732| = 0.018\)
- \(|1.73 - 1.732| = 0.002\)
- \(|1.69 - 1.732| = 0.042\)

### Step 4: Determine the Closest Value
From the comparisons, we see that:
- The difference for \(1.73\) is the smallest (\(0.002\)), making it the closest to \(1.732\).

### Conclusion
Thus, the option that is closest to \(\sqrt{3}\) is \(\frac{173}{100}\) or \(1.73\).