Calculate square roots with step-by-step explanations
Enter any positive number (decimals allowed)
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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 |
|---|---|---|---|
| Newton-Raphson | Iterative method using derivatives | Very High | Fast |
| Babylonian | Ancient iterative averaging method | High | Fast |
| Estimation | Guess and check with refinement | Medium | Medium |
| Prime Factorization | Factor number into primes (perfect squares only) | Exact | Slow |
Square roots of negative numbers are imaginary numbers (not supported in this calculator).