Enter values and select Calculate.
Calculated result
Formula and worked example
The principal square root √x is the nonnegative value whose square equals x. A positive integer radical can be simplified by extracting perfect-square factors.
√144 = 12 exactly. √2 ≈ 1.41421356237. For an integer radical, √72 = √(36 × 2) = 6√2.
Exact and approximate results
Perfect-square integers display an exact equals sign.
Non-perfect squares display a controlled approximation and are not labeled exact.
Supported positive integers also receive a deterministic simplified-radical form when a square factor exists.
Real-number boundary
Negative radicands have no real square root.
This calculator reports that boundary instead of exposing NaN, changing the sign, or inventing a complex result.
Complex-number roots remain outside this calculator.
Related square-root jobs
Exponent Calculator handles general powers and keeps square-root intent here.
Pythagorean Theorem and Right Triangle calculators use square roots inside distinct triangle-solving workflows.
Methodology and limits
This deterministic browser-local tool uses strict complete-value parsing and the displayed mathematical definition. It does not evaluate expressions, execute entered text, call a remote service, or silently cross its documented real-number or integer domain.