Radical Simplifier
Simplify √n by extracting the largest perfect-square factor: √n = a√b.
Inputs
Positive integer
2 for square root, 3 for cube root, etc.
Simplified Form
6√2
Coefficient Outside
6
Remaining Radicand
2
Decimal Value
8.48528137
Step by step
Values used
Number under radical (n) = 72; Root index = 2
Radical simplification
ⁿ√(a^n · b) = a · ⁿ√b
Simplified Form
= 6√2
Coefficient Outside
= 6
Remaining Radicand
= 2
Decimal Value
= 8.48528137
How it works
To simplify a radical, find the prime factorization of the number under the radical. For each prime factor, extract groups of size equal to the root index. For example, √72 = √(36·2) = 6√2, because 72 = 2³·3² and we extract one pair of 3s and one pair of 2s.
Formula
Radical simplification
ⁿ√(a^n · b) = a · ⁿ√b
- a
- Extracted coefficient
- b
- Remaining radicand
- n
- Root index
Frequently Asked Questions
What is a perfect square factor?
A perfect square factor is a factor of the radicand that is itself a perfect square (like 4, 9, 16, 25...). Extracting it simplifies the radical.
Can this simplify cube roots?
Yes — set the root index to 3. For cube roots, it extracts perfect cube factors.