Math

Simplifying radicals.

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 · 4 phases

Step by step.

  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

Real-world.

  • 1 √72 = √(36 × 2) = 6√2
  • 2 √(50x²) = 5x√2
  • 3 Rationalizing: 3/√5 = 3√5/5
Key Fact

√(ab) = √a · √b

Studied in

1 unit use this concept.