🧮 Radical Simplifier

Easily simplify square roots and other radical expressions into their simplest form with instant results and step-by-step breakdown.

Input
Root Type
Options
Quick Examples
Simplified Result

Enter a radical to simplify

Type a number or expression and click "Simplify" to see the simplified radical form.

How It Works

The Radical Simplifier uses prime factorization to break down the radicand (the number inside the radical) into its prime factors. It then groups these factors based on the root index to simplify the expression.

Simplification Steps:
  1. Factor the radicand into its prime factors
  2. Group the factors based on the root index (pairs for square roots, triplets for cube roots, etc.)
  3. For each complete group, move one factor outside the radical
  4. Multiply the factors outside the radical together
  5. Multiply the remaining factors inside the radical together
Example: Simplify √72

1. Prime factorize 72: 2 × 2 × 2 × 3 × 3

2. Group pairs (since it's a square root): (2 × 2) × (3 × 3) × 2

3. For each pair, take one factor outside: 2 × 3 × √2

4. Multiply outside factors: 6√2

Common Examples
Input Simplified Form
√8 2√2
√12 2√3
√18 3√2
√20 2√5
√27 3√3
√32 4√2
√45 3√5
√48 4√3
√50 5√2
√75 5√3