Rational or Irrational

This calculator checks whether a number is rational: a root, a fraction, a decimal or a well-known constant. The solution shows the prime factorization and explains the conclusion.

What “rational” means

A rational number can be written as a fraction p/q with integers p and q. Its decimal expansion is finite or repeating. The expansion of an irrational number is infinite and non-repeating.

How to check a root

The k-th root of a fraction in lowest terms is rational only if the exponents of all primes in the numerator and denominator are divisible by k.

Example. 12 = 2² · 3. The exponent of 3 is 1, which is not divisible by 2, so √12 is irrational. 36 = 2² · 3², so √36 = 6.