Rational numbers have terminating or repeating decimals; irrational numbers, such as √2 and π, go on forever without repeating. The proof that √2 is irrational is one of the oldest in mathematics.
How to use the Rational or Irrational Calculator
- Number to be tested
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Fractions, terminating decimals and repeating decimals (written like 0.1(6)) are rational. √n and ∛n are tested for perfect squares and cubes. π, e and φ are known to be irrational.
Formula
Rational: can be written as p/q with integers p, q (q ≠ 0)
√n is rational only if n is a perfect square
Worked example
Inputs — Number to be tested: sqrt(8).
Results — Rational or irrational? = Irrational; Why = 8 is not a perfect square, so √8 is irrational.; Real or complex = Real number; Sign = Positive.
Key terms
- Rational number
- A ratio of two integers.
- Irrational number
- A real number that is not rational.
Frequently asked questions
Is 0.333… rational?
Yes – it equals 1/3.
Is √16 rational?
Yes, it equals 4.
Is π rational?
No – π is irrational (and transcendental).
Can the sum of two irrationals be rational?
Yes: √2 + (−√2) = 0.