Simplifying Radicals Calculator
Enter a number under the radical and choose the root index to simplify it into its simplest a·ⁿ√b form.
What does simplifying a radical mean?
Simplifying a radical means rewriting an expression like √72 in the form a·√b, where b has no remaining perfect-power factors for the given root index. For example, √72 simplifies to 6√2 because 72 = 36 × 2 and 36 is a perfect square.
How this calculator works
The calculator repeatedly checks for factors that are perfect nth powers (perfect squares for square roots, perfect cubes for cube roots, and so on), pulling each one out from under the radical as a whole-number multiplier. What’s left inside the radical, multiplied by that outside coefficient and the chosen root, is mathematically equal to the original expression.
For an even root index (like square root or 4th root), negative numbers under the radical have no real-number result, so this calculator shows a notice in that case rather than an invalid value.
This calculator is for general educational and reference purposes.