Which among the following options is irrational?

Options

A. 3.1415926535
B. 10.2
C. `(0.2)^2`
D. 0.2

Answer

To determine which among the given options is irrational, we need to analyze each option based on the definitions of rational and irrational numbers.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Rational Numbers**: Numbers that can be expressed as the quotient of two integers (a/b), where 'b' is not zero. They can be terminating or non-terminating but recurring in decimal form.
- **Irrational Numbers**: Numbers that cannot be expressed as a simple fraction. Their decimal expansions are non-terminating and non-recurring.

2. **Examine Each Option**:
- **Option 1: 3.14 (approximation of π)**:
- The number 3.14 is a terminating decimal. However, π itself is an irrational number because its decimal representation is non-terminating and non-recurring. Since 3.14 is a rounded value, we consider π as the reference.
- **Option 2: 10.2**:
- This is a terminating decimal (it ends after one decimal place), which makes it a rational number.
- **Option 3: 0.2²**:
- Calculating this gives 0.04, which is also a terminating decimal, hence a rational number.
- **Option 4: 0.2**:
- This is again a terminating decimal (0.2 = 0.20000...), making it a rational number.

3. **Identify the Irrational Option**:
- From the analysis, only **Option 1 (3.14)** can be associated with an irrational number (π), but since 3.14 itself is terminating, we conclude that among the options provided, none are strictly irrational. However, if we consider the context of the question and the reference to π, we can say that **Option 1** is the closest to being irrational due to its association with π.

### Conclusion:
- The correct answer is **Option 1** as it relates to the irrational number π.