Question

Which of the following is an irrational number: −15/29
, 0.343434..., 2√/3
, or 87.9821?

Answer 1

An irrational number is a number that cannot be expressed as a simple fraction, meaning it cannot be written in the form \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \).

Let's analyze each option:

1. **−15/29**: This is a rational number because it can be expressed as a fraction of two integers.

2. **0.343434...**: This is a repeating decimal (specifically \( 0.\overline{34} \)), and it can also be expressed as a fraction. Therefore, it is rational.

3. **\( 2\sqrt{3} \)**: The square root of 3 is an irrational number (it cannot be expressed as a fraction). Multiplying it by 2 still results in an irrational number. Thus, \( 2\sqrt{3} \) is irrational.

4. **87.9821**: This is a decimal and can be expressed as a fraction (\( \frac{879821}{10000} \)). Therefore, it is a rational number.

From this analysis, the only irrational number among the options provided is:

**\( 2\sqrt{3} \)**.