Question

Toggle whether the expression is rational or irrational

Answer 1

I don’t see an expression to check — please paste the expression you want classified.

While you prepare that, here are quick rules and a checklist you can use to decide whether an expression is rational or irrational:

Rules / checklist
- Integers and ratios of integers (a/b with integers a,b and b ≠ 0) are rational.
- nth root of an integer (or rational) is rational only when the radicand is an exact nth power (e.g., sqrt(9)=3 is rational, sqrt(2) is not).
- A rational multiple of a nonzero irrational is irrational (e.g., 2·√2 is irrational).
- Sum/product of rationals is rational.
- Sum/product of a rational and a nonzero irrational is irrational.
- Sum/product of two irrationals can be rational or irrational (e.g., √2 + (1−√2) = 1 is rational; √2 + √3 is irrational).
- Known transcendental numbers (π, e) are irrational; any nonzero rational multiple or sum with a rational remains irrational.
- For expressions with radicals, simplify and rationalize denominators; check whether radicals reduce to rational numbers (perfect powers).
- If in doubt for algebraic expressions, try to express the number as a fraction of integers; for advanced cases consider minimal polynomials (if it’s root of polynomial with integer coefficients it’s algebraic; many algebraic numbers are irrational but some are rational).

Examples (toggle labels)
- 3 → rational
- 4/7 → rational
- sqrt(9) → rational
- sqrt(2) → irrational
- sqrt(12) = 2·sqrt(3) → irrational
- ∛8 = 2 → rational
- √2 + (1 − √2) → rational
- 2·√2 → irrational
- π + 2 → irrational

Send the specific expression you want checked and I’ll mark it rational or irrational and show a short justification.