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Rational or Irrational Number — result sheet
Classify a fraction or a principal square root as rational or irrational and show the reduced form.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: p/q is rational when p and q are integers with q ≠ 0; √n is rational exactly when n is a perfect square for nonnegative integer n.
Every fraction of integers with a nonzero denominator is rational. For a nonnegative integer under a principal square root, a perfect square produces a whole-number result; otherwise the square root is irrational and can still be simplified by removing square factors.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number form — 2 choices
- Fraction numerator p — minimum -1000000000; maximum 1000000000
- Fraction denominator q — minimum -1000000000; maximum 1000000000
- Square-root radicand n — minimum 0; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Number form | fraction |
| Fraction numerator p | 7 |
| Fraction denominator q | 12 |
| Square-root radicand n | 44 |
Rational; reduced form 7/12; decimal 0.5833333333
Assumptions and limits
- Fraction mode uses integer numerator and denominator values.
- Square-root mode uses the principal real square root of a nonnegative integer.
- The classification is limited to the selected fraction or square-root form and does not classify arbitrary decimal strings or sums of radicals.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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