How to use this calculator
A square root can often be simplified by taking perfect-square factors outside the radical. For example, 72 contains the square factor 36, so its positive square root is 6 times the square root of 2. The remaining radicand has no square factor greater than one.
The method
Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.
Number under the square root: 72
Simplified square root: 6√2
Exact radical form for sqrt(72).
Scope and limitations
Nonnegative integer radicands only. The output is the principal, nonnegative square root. Fractional radicands and complex roots are not supported.
Common questions
Why does sqrt(9) return 3, not +/-3?
The square-root symbol means the principal nonnegative root. The equation x^2 = 9 has two solutions, but sqrt(9) itself is 3.
What is a perfect square?
A number equal to an integer multiplied by itself, such as 0, 1, 4, 9, 16, or 25.
References & further reading
External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.