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:
- −1529: This is an integer, and all integers are rational numbers.
- −1/5: This can be expressed as a fraction, so it is a rational number.
- 0.343434...: This is a repeating decimal (the "34" repeats), so it can be expressed as a fraction, making it a rational number.
- 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.
- 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:
\(2√3\).
1 answer