Decimal to Square Root Calculator
Convert any decimal to its square root with clear steps and flexible precision. Detect perfect squares and exact fraction roots automatically. Export results as CSV or PDF for records and learning anytime.
Developed by: Nohman Habib
Example Data
| Input (x) | √x (Approx.) | Exact Form (when applicable) |
|---|---|---|
| 0.25 | 0.5 | 1/2 |
| 2 | 1.414213… | Not exact (irrational) |
| 12 | 3.464101… | 2√3 |
| 100 | 10 | 10 |
| -9 (complex enabled) | 3 i | 3i |
Formula
The principal square root of a number x is the value r such that:
r = √x and r² = x
If x is negative and complex results are enabled, then:
√(-a) = √a · i, where i² = -1
How to Use This Calculator
- Enter your decimal number x in the input field.
- Choose the number of decimal places for the output.
- Select a rounding mode: Round, Floor, or Ceil.
- If your input may be negative, enable complex results.
- Click Calculate to view the result above the form.
- Use the CSV or PDF buttons to export the latest result.
FAQs
1) What is the square root of a decimal number?
It is the number that, when multiplied by itself, equals the original decimal. For example, √0.25 equals 0.5 because 0.5 × 0.5 = 0.25.
2) Why does √2 have so many digits?
√2 is an irrational number, meaning it cannot be written exactly as a finite decimal or a simple fraction. The calculator shows an approximation based on your chosen precision.
3) Can this calculator show an exact answer?
Yes, when the input is a perfect square or a perfect-square fraction, it can show an exact form such as 10 or 1/2. Otherwise it returns a rounded approximation.
4) What happens if I enter a negative decimal?
If complex results are disabled, there is no real square root and the calculator will show an error. If enabled, it returns an imaginary result like 3i for √(-9).
5) What rounding mode should I use?
Use Round for standard rounding. Use Floor to always round down, and Ceil to always round up. These are helpful when you must stay under or over a tolerance.
6) Why does (√x)² not always match x exactly?
When you limit decimal places, you are rounding the square root. Squaring a rounded value introduces small error. Increasing decimal places reduces the difference.