Radical Form Calculator (Simplify Radicals)
Simplify square and nth roots to exact radical form, with the decimal value.
Enter your values
Results update instantly as you type — no submit needed.
Results
- Simplest radical form
- 6√2
- Decimal value
- 8.48528137
- Perfect-power factor removed
- 6^2 = 36
- Remaining radicand
- 2
Working
- 1Factor out the largest perfect square: 72 = 36 × 2
- 2Take the root of the perfect power: √36 = 6
- 3Result: 6√2
Quick answer
To write a number in simplest radical form, factor the radicand and pull out every perfect power matching the index. For example √72 = √(36·2) = 6√2.
c·ⁿ√(pⁿ·m) = c·p·ⁿ√m
How to use the Radical Form Calculator
- 1Enter the number under the radical and the index.
- 2Add a coefficient if your expression has one.
- 3Read the exact simplified radical plus the decimal value.
Frequently asked questions
What is simplest radical form?
A radical is in simplest form when the radicand has no factor that is a perfect power of the index, no fractions remain under the root and no radicals sit in a denominator.
How do you simplify √72?
72 = 36 × 2 and 36 is a perfect square, so √72 = √36 · √2 = 6√2 ≈ 8.4853.
Can I simplify cube roots?
Yes — set the index to 3 (or any integer ≥ 2) and the calculator pulls out perfect cubes or higher powers.