Updated: July 2026
What is the Square Root Calculator
Square Root Calculator is a free online tool that calculates the square root, cubic root or the root of any index of a number, showing both the approximate decimal value and the simplified algebraic form. It was created especially for students: if you type the square root of 20 on a common calculator, the result comes as 4.4721359..., but teachers usually require the simplified answer, in the format 2√5. Our tool delivers both.
To do this, the system factors the number into prime factors and separates what can leave the root from what needs to remain within it, exactly as taught in school. It works with any root index, not just the square root, which is useful both for those studying for the Enem and university entrance exams and for those who just need a quick day-to-day calculation.
How to use the Square Root Calculator
- Enter the radicand, that is, the number that is inside the root.
- Choose the root index: Square, Cubic or a custom index (4, 5, 6...).
- Adjust, if desired, the number of decimal places displayed in the approximate result.
- See the result: when the root is exact, the tool shows the correct integer; when it is not exact, it shows the simplified form, such as
2√5, next to the decimal approximation. - Follow the complete factorization step by step, displayed as if it were a teacher's whiteboard.
Roots of negative numbers
An important detail: there is no even index root, such as the square root, of a negative number within the set of real numbers, and the calculator warns you when this happens. The odd index root, such as the cubic root, of a negative number normally exists and also results in a negative number. The tool handles these cases automatically, so you don't have to worry about manually finding out if that root is possible or not.