If `sqrt3=1.732`, then the value of `(sqrt3+1)/(sqrt3-1)` is

Options

A. `3.732`
B. `(1)/(3.732)`
C. `0.732`
D. `2.732`

Answer

To solve the problem, we need to find the value of \(\frac{\sqrt{3}+1}{\sqrt{3}-1}\) given that \(\sqrt{3} = 1.732\).

### Step-by-Step Solution:

1. **Write the Expression**:
We start with the expression:
\[ \frac{\sqrt{3}+1}{\sqrt{3}-1} \]

2. **Rationalize the Denominator**:
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is \((\sqrt{3}+1)\):
\[ \frac{(\sqrt{3}+1)(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)} \]

3. **Apply the Difference of Squares**:
The denominator can be simplified using the difference of squares formula \(a^2 - b^2\):
\[ (\sqrt{3})^2 - (1)^2 = 3 - 1 = 2 \]
So, the denominator becomes \(2\).

4. **Expand the Numerator**:
Now, we expand the numerator:
\[ (\sqrt{3}+1)(\sqrt{3}+1) = (\sqrt{3})^2 + 2(\sqrt{3})(1) + (1)^2 = 3 + 2\sqrt{3} + 1 = 4 + 2\sqrt{3} \]

5. **Combine the Results**:
Now we can combine the results:
\[ \frac{4 + 2\sqrt{3}}{2} \]

6. **Simplify the Expression**:
We can simplify this by dividing both terms in the numerator by \(2\):
\[ = 2 + \sqrt{3} \]

7. **Substitute the Value of \(\sqrt{3}\)**:
Now we substitute \(\sqrt{3} = 1.732\):
\[ = 2 + 1.732 = 3.732 \]

### Final Answer:
Thus, the value of \(\frac{\sqrt{3}+1}{\sqrt{3}-1}\) is:
\[ \boxed{3.732} \]