What Is Simplest Radical Form?
A radical expression is in its simplest form when the radicand (the number under the radical sign) has no perfect square factors other than 1. Simplifying radicals makes expressions easier to work with and is required in most algebra courses.
1. Find the largest perfect square that divides n
2. Factor: √n = √(a² × b) = a√b
Example: √72 = √(36 × 2) = 6√2
Step-by-Step Process
To simplify a radical: factor the radicand into its prime factors, group pairs (for square roots), bring pairs outside the radical, and multiply remaining factors inside.
Example: √200 = √(4 × 50) = √(4 × 25 × 2) = 2 × 5 × √2 = 10√2
Radical Rules
- √(ab) = √a × √b (product rule)
- √(a/b) = √a / √b (quotient rule)
- (√a)² = a
- √a × √a = a
Applications
Simplifying radicals is essential in algebra, geometry (distance formulas, Pythagorean theorem), trigonometry, and calculus. It is also required on standardized tests like the SAT and ACT.
How to Use
Enter any positive integer to find its simplest radical form. The calculator factors the number and shows the simplified expression in real time.
Special Cases
Perfect squares (4, 9, 16, 25, ...) simplify completely with no radical remaining. Prime numbers cannot be simplified further and remain under the radical sign.