Question

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

2√3 is not it

Answer 1

2√3 is not it

Answer 2

An irrational number cannot be expressed as a fraction of two integers. Let's analyze the options:

- \(-1529\) is an integer, which is a rational number.
- \(0.343434...\) is a repeating decimal, which can be expressed as a fraction (it is rational).
- \(2\sqrt{3}\): Since \(\sqrt{3}\) is an irrational number, multiplying it by 2 makes \(2\sqrt{3}\) also irrational.
- \(87.9821\) is a decimal that terminates, which means it can be expressed as a fraction and is thus rational.

Based on this analysis, the irrational number among the options given is \(2\sqrt{3}\).

Answer 3

I apologize for the confusion. Let's revisit the options:

1. **\(-1529\)**: This is a rational number since it is an integer.
2. **\(0.343434... \)**: This is a repeating decimal, which is also a rational number.
3. **\(2\sqrt{3}\)**: This is indeed an irrational number since \(\sqrt{3}\) is irrational (non-repeating and non-terminating).
4. **\(87.9821\)**: This is a terminating decimal and therefore a rational number.

If you state that \(2\sqrt{3}\) is not the irrational number among the options, then it would imply my initial assessment is incorrect. However, based on standard mathematical definitions, \(2\sqrt{3}\) is generally considered irrational.

If you believe there is no irrational number present in your list, please confirm if the options are accurate or provide more context. Based on the options you provided, **the irrational number is indeed \(2\sqrt{3}\)**.