Question

Which of the following is an irrational number: −1529
−
1
5
29
, 0.343434..., 2√3
2
3
, or 87.9821?

Answer 1

To determine which of the given numbers is an irrational number, we need to recall the definitions of rational and irrational numbers.

- A rational number can be expressed as the fraction of two integers (i.e., in the form \(\frac{a}{b}\), where \(a\) and \(b\) are integers, and \(b \neq 0\)).
- An irrational number cannot be expressed as a simple fraction; instead, its decimal representation is non-terminating and non-repeating.

Now, let's evaluate each of the given numbers:

1. **−1529**: This is an integer, and all integers are rational numbers.
2. **−1/5**: This can be expressed as a fraction, so it is a rational number.
3. **0.343434...**: This is a repeating decimal (the "34" repeats), so it can be expressed as a fraction, making it a rational number.
4. **2√3**: The square root of 3 is known to be an irrational number (it cannot be expressed as a fraction). Therefore, \(2√3\) is also irrational because multiplying a rational number (2) by an irrational number results in an irrational number.
5. **87.9821**: This is a terminating decimal, which means it can be expressed as a fraction, so it is a rational number.

Among the numbers listed, the one that is irrational is:

**\(2√3\)**.