Which number is irrational?
- (correct answer)
Explanation: Understanding irrational numbers means recognizing that they cannot be expressed as fractions a/b where a and b are integers and b ≠ 0, and their decimal expansions are non-terminating and non-repeating, like √2 or π, while rational numbers can be expressed as such fractions and have terminating or repeating decimals. Rational numbers include integers like 5 (which is 5/1), fractions like 3/4, terminating decimals like 0.5 (which is 1/2), and repeating decimals like 0.333... (which is 1/3 with the '3' repeating). Irrational numbers, however, cannot be written as fractions, and their decimals go on forever without a repeating pattern, such as √2 ≈ 1.41421356... or π ≈ 3.14159265.... Examples include √9 = 3, which is rational as it's a perfect square, while √2 is irrational since it's not a perfect square; 0.666... is rational as it equals 2/3, but π is irrational with no repeating pattern. The irrational number is √3 because 3 is not a perfect square, so its decimal is non-terminating and non-repeating, while √25 = 5 = 5/1, 7/8 = 0.875, and 0.4 = 2/5 are all rational. A common error is thinking all square roots are irrational, but perfect squares like √25 are rational; another is assuming repeating decimals like 0.333... are irrational when they're rational, or that π = 22/7 exactly. To classify square roots: perfect square means rational, non-perfect means irrational; convert repeating decimals to fractions to confirm rational; avoid mistaking fractions or terminating decimals for irrational.