Simplify Radical Calculator
Enter a whole number to simplify its square root.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Divide out the repeated prime factors in pairs
- Each pair moves outside the root as a single factor
- Whatever is left stays inside the root
For prime factors, use the prime factorization calculator. For other roots, see the root calculator.
Worked example
√72:
- 72 = 2 × 2 × 2 × 3 × 3 = (2 × 3)² × 2
- √72 = 6√2, which is about 8.4853
Why your number may differ
This simplifies square roots only. Cube roots and higher roots follow the same idea with groups of 3 or more.
Frequently asked questions
How do you simplify a square root?
Find the largest perfect square that divides the number, take its square root outside, and leave the rest inside. √72 = √(36 × 2) = 6√2.
What if there is no square factor?
Then it is already in simplest form. √17 stays as √17.
What if the number is a perfect square?
The root comes out as a whole number, so √49 = 7.