Fraction Square Root Calculator
Calculate the square root of any fraction or mixed number with exact simplified radicals and decimals. See step by step reduction and rationalization. Export results to CSV or PDF for homework checks notes or calculations.
Developed by: Nohman Habib
Example Data
| Input (Mixed or Fraction) | As Fraction | Exact √(fraction) | Decimal (approx.) |
|---|---|---|---|
| 1 1/4 | 5/4 | √5/2 | 1.1180 |
| 0 8/9 | 8/9 | 2√2/3 | 0.9428 |
| 2 3/16 | 35/16 | √35/4 | 1.4790 |
| -0 1/9 (imag enabled) | -1/9 | i/3 | i × 0.3333 |
Formula
- Convert mixed number to improper fraction: (whole × denominator + numerator) / denominator
- Reduce the fraction: n/d (divide by GCD)
- Square root rule: √(n/d) = √n / √d (for d > 0)
- Simplify radicals by extracting perfect squares and rationalize the denominator when needed
- Negative input: √(-x) = i × √(x) (only when imaginary mode is enabled)
How to Use This Calculator
- Enter the whole number (optional) if you have a mixed number.
- Enter the numerator and denominator for the fraction part.
- Choose the number of decimal places you want.
- If your fraction may be negative, enable imaginary results.
- Click Calculate to see the simplified exact answer and steps.
- Use Download CSV or Download PDF to export the results.
FAQs
1) Can this simplify square roots like √(8/9)?
Yes. It reduces the fraction and extracts perfect squares to give a simplified radical result, such as 2√2/3, plus a decimal approximation to your chosen precision.
2) What if my input is already a perfect square fraction?
If the numerator and denominator are perfect squares, the calculator returns a rational number. For example, √(49/64) becomes 7/8 after simplification.
3) Why do you rationalize the denominator?
Rationalizing removes radicals from the denominator, which is the common “simplified” math form. The value does not change, only the presentation becomes cleaner.
4) Can I enter a mixed number like 2 3/16?
Yes. Put 2 in the whole field and 3 and 16 in numerator and denominator. The calculator converts it to 35/16 first, then applies the square root steps.
5) What happens if I enter a negative fraction?
If imaginary mode is off, the calculator warns because the real square root is undefined. If imaginary mode is on, it returns an i × (positive root) result.
6) What do the CSV and PDF downloads include?
They export your inputs, the reduced fraction, the exact simplified result, the decimal approximation, and whether the result is real or imaginary, so you can save or share the calculation.