Simplify Radical Calculator
Enter a number under a square root to simplify it into its simplest radical form — pulling out the largest perfect square factor instead of leaving an unsimplified root.
Simplified form
—
Enter a number to simplify.
How the Simplify Radical formula works
Finding the largest perfect square factor:
√n = √(a² × b) = a√b, where a² is the largest perfect square dividing n evenly
Step-by-step calculation
- Find the largest perfect square (4, 9, 16, 25, ...) that divides the number evenly.
- Split the number into that perfect square times a remaining factor.
- Take the square root of the perfect square part to pull it outside the radical, leaving the remaining factor underneath.
Worked example
√72: the largest perfect square factor of 72 is 36 (72 = 36 × 2). √72 = √36 × √2 = 6√2 — the simplified radical form.
Frequently asked questions
What if the number has no perfect square factors?
Then the radical is already in simplest form — for example, √15 can't be simplified further since 15 has no perfect square factors other than 1.
Does this work for cube roots too?
This calculator specifically simplifies square roots. Cube roots and higher roots use the same underlying idea (pulling out perfect cube or higher-power factors) but require a separate calculation.