Question

Which of the following is an irrational number: −1 5/29 , 0.343434..., 2√/3 , or 87.9821?

Answer 1

To determine which of the given numbers is irrational, let's analyze each one:

1. **−1 5/29**: This is a mixed number. It can be converted to an improper fraction or expressed as a decimal. Since both parts (the whole number and the fractional part) are rational, this number is rational.

2. **0.343434...**: This is a repeating decimal. Any decimal that repeats can be expressed as a fraction, which means it is rational.

3. **2√/3**: The notation seems to be a bit unclear, but if we interpret it as \( \frac{2\sqrt{3}}{3} \), we can analyze it. The square root of 3 is irrational, and multiplying an irrational number (√3) by a rational number (2/3) results in an irrational number. Thus, \( \frac{2\sqrt{3}}{3} \) is irrational.

4. **87.9821**: This is a finite decimal, which can be expressed as a fraction (for example, \( 879821/10000 \)). Therefore, it is rational.

Based on this analysis, the only irrational number in the list is **2√/3** (assuming it's interpreted as \( \frac{2\sqrt{3}}{3} \)).