Calculator Form
Use the optional whole part for mixed numbers like 1 3/4. Leave it as 0 for ordinary fractions.
Formula Used
√(n/d) = √n / √d
a b/c = (a×c + b) / c
√(k²m) = k√m
(x√p)/(√q) = x√(pq)/q
How the calculator works
- It converts any mixed number into an improper fraction.
- It simplifies the fraction before finding the square root.
- It extracts perfect-square factors from numerator and denominator.
- It shows an exact radical form and a decimal approximation.
- It checks the result by squaring the rounded decimal value.
How to Use This Calculator
- Enter the whole part only if your value is a mixed number.
- Enter the numerator and denominator of the fraction.
- Choose decimal places, graph scale, and rounding mode.
- Press Calculate Square Root to show the result above the form.
- Review the exact radical form, decimal value, graph, and steps.
- Use the CSV and PDF buttons to export the current report.
Example Data Table
| Entered Value | Simplified Fraction | Exact Result | Decimal Approximation |
|---|---|---|---|
| 1/4 | 1/4 | 1/2 | 0.500000 |
| 2/3 | 2/3 | √6/3 | 0.816497 |
| 9/16 | 9/16 | 3/4 | 0.750000 |
| 1 7/9 | 16/9 | 4/3 | 1.333333 |
| 12/5 | 12/5 | √15/5 × 2 | 1.549193 |
Note: The live calculator returns the exact simplified form automatically. The table is included as a study reference.
FAQs
1. What values can this calculator handle?
It accepts proper fractions, improper fractions, and mixed numbers entered through the whole part, numerator, and denominator fields. All values must be non-negative, and the denominator must be greater than zero.
2. Why do I see both an exact result and a decimal result?
The exact result preserves radicals and fractions without rounding. The decimal result gives a practical approximation for everyday use, measurement work, graphing, and quick comparisons.
3. Why is the denominator sometimes removed from the radical?
That process is called rationalization. It rewrites the exact result so the denominator is a whole number, which is a cleaner and more standard final form in algebra.
4. Can it simplify mixed numbers before taking the square root?
Yes. A mixed number like 1 3/4 is first converted into an improper fraction, simplified if possible, and then processed through the square-root steps.
5. What happens if the fraction is already a perfect-square fraction?
The calculator returns a rational answer, such as 3/4 from 9/16. In those cases, the exact and decimal outputs match without any remaining radical part.
6. Why is my squared check slightly different from the original value?
The squared check uses the rounded decimal result, not the unrounded exact value. Small differences are normal whenever decimal rounding is applied.
7. What does the Plotly graph show?
It plots how the square root changes as the fraction value is multiplied by a scaling factor. This helps visualize growth and compare root behavior across related values.
8. Can I export the calculation for records or sharing?
Yes. Use the CSV button for spreadsheet-friendly rows and the PDF button for a clean summary containing inputs, outputs, and the step-by-step breakdown.