Calculator Form
Formula Used
The principal square root of a decimal n is the non-negative value x that satisfies x² = n.
x = √n
If the decimal can be written as a fraction, the square root rule becomes:
√(p/q) = √p / √q
Then perfect-square factors are pulled outside the radical to create a simpler exact form. When needed, the denominator is rationalized for a cleaner algebraic expression.
How to Use This Calculator
- Enter a decimal value greater than or equal to zero.
- Choose the number of decimal places you want in the displayed root.
- Pick a rounding mode and your preferred number display style.
- Set graph limits and points if you want a wider or smoother curve.
- Submit the form to see the result above the calculator.
- Use the CSV button for data export and the PDF button for a quick summary file.
Example Data Table
| Decimal input | Fraction form | Simplified square root | Decimal result |
|---|---|---|---|
| 0.04 | 1/25 | 1/5 | 0.2 |
| 0.50 | 1/2 | √2/2 | 0.707107 |
| 2.25 | 9/4 | 3/2 | 1.5 |
| 7.2 | 36/5 | 6√5/5 | 2.683282 |
| 12.96 | 324/25 | 18/5 | 3.6 |
FAQs
1. What does this calculator do?
It finds the principal square root of a decimal number. It also converts the decimal to a fraction, simplifies the radical when possible, checks the result, and draws a matching square-root graph.
2. Can it simplify decimals into exact radicals?
Yes. When the decimal can be expressed cleanly as a fraction, the calculator simplifies the radical by removing perfect-square factors. Values such as 0.5 become forms like √2/2 instead of only a rounded decimal.
3. Why do some answers stay irrational?
Many decimals do not produce rational square roots. The calculator still shows a simplified radical form and a decimal approximation. That keeps the exact structure visible while also giving a practical working value.
4. What happens with negative decimals?
This page focuses on real-number square roots, so negative decimals are rejected. In complex-number work, a negative input would involve imaginary values, which are outside this calculator’s present scope.
5. Why is a fraction shown before the root?
Fractions make simplification easier. A decimal such as 2.25 becomes 9/4, and √(9/4) simplifies immediately to 3/2. That exact route is clearer than working only with rounded decimals.
6. What does the squared check mean?
The squared check raises the displayed square root back to the power of two. It shows how closely the rounded result returns to your original decimal and helps you judge rounding impact.
7. When should I use scientific notation?
Scientific notation is useful for very small or very large values. It makes long decimals easier to read while preserving scale, especially in technical, engineering, and research-style calculations.
8. What do the CSV and PDF buttons export?
The CSV export downloads the calculated fields as rows. The PDF button creates a concise result summary you can save, share, or print after a calculation is completed.