MathIsimple
Radical Calculator

Radical Calculator

Simplify square roots, cube roots, and nth roots with step-by-step solutions using prime factorization and simplification methods.

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Calculator
Enter the values for your radical expression: y⋅xny \cdot \sqrt[n]{x}

Default: 1

2 = square root, 3 = cube root, etc.

Number under the radical sign

Common Radical Examples
Try these popular radical simplification examples
122\sqrt[2]{12}
=
232\sqrt{3}
243\sqrt[3]{24}
=
2332\sqrt[3]{3}
25022\sqrt[2]{50}
=
10210\sqrt{2}
325\sqrt[5]{32}
=
22
What is a Radical?

A radical is a mathematical expression that uses a root symbol (√) to indicate the nth root of a number. The general form is sqrt[n]x\\sqrt[n]{x}, where:

  • n is the root index (2 for square root, 3 for cube root, etc.)
  • x is the radicand (the number under the radical sign)
  • When n = 2, we write sqrtx\\sqrt{x} (square root)
  • When n = 3, we write sqrt[3]x\\sqrt[3]{x} (cube root)

Example: sqrt[5]32=2\\sqrt[5]{32} = 2 because 25=322^5 = 32

How to Simplify Radicals?

Method 1: Prime Factorization

  1. Find the prime factorization of the radicand
  2. Group factors into sets of n (root index)
  3. Extract perfect nth powers from under the radical
  4. Multiply by any coefficient outside

Method 2: Step-by-Step Simplification

  1. Identify perfect nth power factors
  2. Extract these factors from the radical
  3. Combine with the coefficient
  4. Leave remaining factors under the radical
Why Use Our Radical Calculator?

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Prime factorization and simplification approaches

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