Enter a fraction
Choose an input type, calculation options, and output precision.
Calculation history
Recent calculations remain in this browser only.
Formula used
√(a/b) = √a / √b, where b ≠ 0.
√a / √b = √(ab) / b, when rationalising.
√(-a/b) = i√(a/b), for positive a and b.
How to use this calculator
- Select fraction, mixed-number, or decimal input.
- Enter the required values carefully.
- Choose exact, decimal, or combined output.
- Enable rationalisation or complex results when needed.
- Press the calculation button to view detailed steps.
- Copy, print, or download the completed result.
Example calculations
| Fraction | Exact result | Simplified result | Type |
|---|---|---|---|
| 9/16 | √(9/16) | 3/4 | Rational |
| 8/18 | √(4/9) | 2/3 | Rational after reduction |
| 5/9 | √(5/9) | √5/3 | Irrational |
| 3/8 | √(3/8) | √6/4 | Rationalised radical |
| -4/25 | i√(4/25) | 2i/5 | Pure imaginary |
Understanding fraction square roots
Perfect-square fractions
A fraction is perfect-square when both parts are squares. Its square root becomes another rational fraction. Reduction can reveal a hidden perfect-square fraction.
Irrational fraction roots
Unpaired prime factors remain inside a radical. These results cannot become terminating exact decimals. A decimal approximation remains useful for comparison.
Negative fraction roots
Negative fractions have no real square roots. Their principal roots use the imaginary unit i. Enable complex results before calculating these values.
Frequently asked questions
1. Can every fraction have a square root?
Every nonnegative fraction has a real square root. Negative fractions require complex numbers.
2. Why should the fraction be reduced first?
Reduction removes common factors. It often reveals simpler radicals or perfect squares.
3. What is a perfect-square fraction?
Its reduced numerator and denominator are perfect squares. The root is rational.
4. Why rationalise the denominator?
Rationalisation removes radicals from denominators. Many courses prefer this standard form.
5. Can I enter a mixed number?
Yes. The calculator converts it into an improper fraction automatically.
6. Can I enter a decimal?
Yes. Standard decimals become exact fractions before square-root simplification.
7. What does i mean?
The symbol i equals the square root of negative one. It represents imaginary numbers.
8. Why does the decimal differ slightly?
Irrational roots have endless decimals. Display precision controls the visible rounding.
9. Are calculation histories uploaded?
No. History uses local browser storage and stays on your device.