Calculate and Simplify Radicals
Enter a coefficient, radicand, and root index. You can also add or subtract two radicals.
Radical Simplifier Examples
How to Simplify a Radical
1. Identify the root index
A square root has index 2, a cube root has index 3, and a fourth root has index 4.
2. Find a perfect-power factor
For √(72), write 72 as 36 × 2. Since 36 is a perfect square, √(72) = 6√(2).
3. Apply the coefficient
For 3√(12), simplify √(12) to 2√(3), then multiply the coefficient: 3 × 2√(3) = 6√(3).
4. Combine like radicals
Radicals can be added or subtracted when their simplified root parts match. For example, 2√(3) + 4√(3) = 6√(3).
Frequently Asked Questions
What is a radical simplifier?
It rewrites a root expression in a simpler equivalent form by extracting perfect powers from inside the radical.
Can I simplify cube roots?
Yes. Set the root index to 3. The calculator supports integer root indices from 2 through 10.
Why does the answer use symbols such as ∛ and ⁴√?
These are Unicode mathematical symbols for cube roots and higher roots. They make the result easier to read without requiring special fonts or a math-rendering library.
Can I use negative radicands?
Negative radicands are accepted for odd roots. Negative radicands with even root indices are rejected because they do not produce real-number results.
Why can't every pair of radicals be combined?
Only like radicals can be combined. For example, √(2) + √(3) stays as two terms because their radicands differ.