Calculate square roots with multiple methods, visualizations, and detailed explanations
Enter any positive number (decimals allowed)
Select calculation precision
The square root of a number is a value that, when multiplied by itself, gives the original number.
Notation: √x or x½
Example: √25 = 5 because 5 × 5 = 25
Property: √(a × b) = √a × √b
| Method | Description | Accuracy | Speed | Best For |
|---|---|---|---|---|
| Newton-Raphson | Iterative method using derivatives | Very High | Fast | General use |
| Babylonian | Ancient iterative averaging method | High | Fast | Large numbers |
| Estimation | Guess and check with refinement | Medium | Medium | Educational purposes |
| Binary Search | Divide and conquer approach | High | Medium | Precise calculations |
Square roots of negative numbers are imaginary numbers (not supported in this calculator).