Radical Form Calculator (Simplify Radicals)
Simplify square and nth roots to exact radical form, with the decimal value.
Enter your values
Enter the coefficient outside the radical you are working with.
Enter the radicand (number under the root) you are working with.
Enter the index (2 = square root) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Simplify square and nth roots to exact radical form, with the decimal value. |
|---|---|
| Category | Math |
| Inputs needed | Coefficient outside the radical, Radicand (number under the root), Index (2 = square root) |
| Main output | Simplest radical form |
| Formula | c·ⁿ√(pⁿ·m) = c·p·ⁿ√m |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Coefficient outside the radical
- Enter the coefficient outside the radical you are working with.
- Radicand (number under the root)
- Enter the radicand (number under the root) you are working with.
- Index (2 = square root)
- Enter the index (2 = square root) you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Coefficient outside the radical1
- Radicand (number under the root)72
- Index (2 = square root)2
Results
- Simplest radical form6√2
- Decimal value8.48528137
- Perfect-power factor removed6^2 = 36
- Remaining radicand2
- Factor out the largest perfect square: 72 = 36 × 2
- Take the root of the perfect power: √36 = 6
- Result: 6√2
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.
What do I need to enter into the Radical Form Calculator?
Just 3 values: coefficient outside the radical, radicand (number under the root), index (2 = square root). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Radical Form Calculator work out the 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. It applies the formula c·ⁿ√(pⁿ·m) = c·p·ⁿ√m and shows the working so you can check each step by hand.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.