Radical Calculator

Radical Calculator

Simplify radicals by extracting perfect powers and compare the exact form with the decimal approximation.

Last updated: June 2026 | By Patchworkr Team

Calculation steps
Find the largest perfect 2th-power factor of 72.
Split out 6 and leave 2 under the radical.
Decimal approximation = 8.485281
Simplified radical
6 * sqrt(2)
Coefficient
6
Radicand
2
Decimal value
8.485281

What Is A Radical?

A radical expression represents an index root, such as a square root, cube root, or higher root. Simplifying a radical means factoring out any perfect powers that can be written outside the radical symbol.

This calculator focuses on whole-number radicands and integer indices so the result stays exact and easy to verify.

How To Simplify A Radical

  1. Choose the radical index, such as 2 for a square root.
  2. Find the largest perfect power that divides the radicand.
  3. Move the perfect-power factor outside the radical.
  4. Leave the leftover factor inside the radical.
simplified form = coefficient x root(radicand)

Worked Example

For sqrt(72), the simplified form is 6 sqrt(2).

72 = 36 x 2
sqrt(72) = sqrt(36) x sqrt(2)
sqrt(72) = 6 sqrt(2)

Frequently Asked Questions

Can the index be 1?

No. Index 1 does not form a radical expression, so the calculator requires an index of at least 2.

Does the calculator accept negative radicands?

Not in this version. It is designed for non-negative integer radicands.

What happens if the radicand is 0?

The result is 0 because zero stays zero under radical simplification.

Can I simplify cube roots?

Yes. Enter 3 as the index to simplify cube roots.

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