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.
- Factor the number under the radical into its prime factors or identify perfect square factors.
- Pull out any perfect square factors as their square root.
- Rationalize the denominator if a radical appears there.
- 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