Which is the odd one out of the following?

Options

A. `sqrt(3)`
B. `(sqrt(3)-1)/(sqrt(3)+1)`
C. `(1/2)^(-2)`
D. `sqrt(17)/8`

Answer

To solve the problem of identifying the odd one out from the given options, we will analyze each option step by step.

### Step 1: Identify the options
The options given are:
1. \( \sqrt{3} \)
2. \( \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \)
3. \( \frac{1}{2^{-2}} \)
4. \( \sqrt{17} \)

### Step 2: Analyze each option
**Option 1: \( \sqrt{3} \)**
- This is a square root of a non-perfect square, which is an irrational number.

**Option 2: \( \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \)**
- To simplify this, we can multiply the numerator and denominator by the conjugate of the denominator:
\[ \frac{(\sqrt{3} - 1)(\sqrt{3} - 1)}{(\sqrt{3} + 1)(\sqrt{3} - 1)} = \frac{(\sqrt{3} - 1)^2}{(\sqrt{3})^2 - (1)^2} = \frac{3 - 2\sqrt{3} + 1}{3 - 1} = \frac{4 - 2\sqrt{3}}{2} = 2 - \sqrt{3} \]
- This is also an irrational number.

**Option 3: \( \frac{1}{2^{-2}} \)**
- This can be simplified:
\[ \frac{1}{2^{-2}} = 2^2 = 4 \]
- This is an integer.

**Option 4: \( \sqrt{17} \)**
- This is also a square root of a non-perfect square, which is an irrational number.

### Step 3: Conclusion
Now we have:
- Option 1: \( \sqrt{3} \) (irrational)
- Option 2: \( 2 - \sqrt{3} \) (irrational)
- Option 3: \( 4 \) (integer)
- Option 4: \( \sqrt{17} \) (irrational)

Since options 1, 2, and 4 are irrational numbers, while option 3 is an integer, the odd one out is:
**Option 3: \( \frac{1}{2^{-2}} \)**, which simplifies to \( 4 \).

### Final Answer
The odd one out is **Option C: \( \frac{1}{2^{-2}} \)**.

---