Simplifying radicals

Math

Definition

The process of rewriting a radical expression in its simplest form by removing perfect square (or higher) factors from under the radical sign. A radical is fully simplified when no perfect square factors remain under the radical and no radicals appear in the denominator.

How It Works

  1. Factor the number under the radical into its prime factors or identify perfect square factors.
  2. Pull out any perfect square factors as their square root.
  3. Rationalize the denominator if a radical appears there.
  4. Combine like radical terms if applicable.

Examples

  • √72 = √(36 × 2) = 6√2
  • √(50x²) = 5x√2
  • Rationalizing: 3/√5 = 3√5/5
Key Fact

√(ab) = √a · √b

Related Terms

Operations with radicals Nth roots Rational exponents Solving radical equations

Study This Concept

Practice simplifying radicals with free review games in these units:

Algebra 1 Unit 9: Radical Expressions