Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityEasy
Which of the following numbers is an irrational number?
- Asqrt(16)
- B2/7
- C0.333...
- Dsqrt(5)
Show answer & explanationAnswer & explanation
Correct answer: D. sqrt(5)
An irrational number is a real number that cannot be expressed as a simple fraction (a/b) of two integers. 0.333... is 1/3 (rational). sqrt(16) is 4 (rational). 2/7 is already a fraction (rational). sqrt(5) cannot be expressed as a simple fraction and its decimal representation is non-repeating and non-terminating, making it irrational.
Why the other options are wrong
- A. This is a perfect square, so its square root is an integer (4), which is a rational number.
- B. This is a fraction of two integers, which is the definition of a rational number.
- C. This is a repeating decimal, which is a rational number (1/3).
Irrational Numbers
Real numbers that cannot be expressed as a simple fraction (a/b) where 'a' and 'b' are integers and 'b' is not zero. Their decimal representations are non-terminating and non-repeating.
- Examples include pi (π) and square roots of non-perfect squares (e.g., √2, √5).
- Rational numbers include integers, fractions, and terminating or repeating decimals.
- Irrational numbers are a subset of real numbers.
Memory trick: Rational is neat and complete, irrational never repeats!