How this calculation works
The principal square root is the non-negative value that gives the input when multiplied by itself. Negative inputs have no real square root.
Result = √numberA worked example
The square root of 144 is 12.
Good to know
Uses the stated formula and assumptions. Displayed decimal values are rounded; use consistent units for all inputs.
One displayed root, two solutions to some equations
The principal square root of 25 is 5. But the equation x² = 25 has two real solutions, 5 and −5, because both squares equal 25. This calculator returns the principal non-negative root, not the entire solution set of an equation.
Geometry gives an intuitive interpretation: a square with area 25 square units has side length 5 units. The square root reverses the squaring of a length, including the change from squared units back to ordinary length units.
Rounded roots are not exact identities
Not every root has a terminating decimal representation. √2 is irrational, so any finite decimal display is an approximation. Squaring the rounded display may produce a value slightly different from 2 even when the internal calculation is appropriate.
Negative inputs have no real square root. Complex-number calculations use a different number system and are outside this tool’s scope.
A few questions, answered
Why is the answer never negative?
The square-root symbol denotes the principal non-negative real root.
Is the square root of 0 allowed?
Yes. The square root of zero is zero.