Radical Expression Simplifier

About this calculator

Simplifying an nth root means factoring the radicand (the number under the root) to pull out any perfect nth powers, leaving the smallest possible number inside the radical. For a square root, this means finding the largest perfect-square factor: √50 = √(25 × 2) = √25 × √2 = 5√2, since 25 is a perfect square but 2 has no square factors left to extract. The same logic extends to cube roots and higher: ∛54 = ∛(27 × 2) = 3∛2, because 27 = 3³ is a perfect cube.

Simplified radical form is the standard way to express irrational answers exactly (rather than as a rounded decimal), which matters for exact arithmetic, further algebraic manipulation, and matching answer keys. Algebra and geometry students, standardized-test takers, and math teachers use this tool to check simplification steps on problems involving the Pythagorean theorem, quadratic formula solutions, or any expression that naturally produces an irrational root.