Math
Square Root Simplifier
Simplify square roots, cube roots and fourth roots to simplest radical form, with the working shown.
Simplest form
6√2
- As a decimal
- 8.48528137
√72 simplifies to 6√2 (about 8.485281).
How it's worked out
- Find the largest perfect power factor
72 = 36 × 236 = 6² - Take it out of the root6√2
How it works
√(a² × b) = a√b
The number is broken into prime factors; each pair (or triple, for a cube root) comes out of the root.
Worked example
72 = 2³ × 3². One pair of 2s and the pair of 3s come out as 2 × 3 = 6, leaving one 2 inside: √72 = 6√2 ≈ 8.485.
Questions people ask
How do I simplify √72?
Find the largest perfect square that divides 72, which is 36. Then √72 = √(36 × 2) = 6√2.
How do I simplify a cube root?
Take out the largest perfect cube: ∛54 = ∛(27 × 2) = 3∛2.
When can't a root be simplified?
When the number has no square factor other than 1, like √7 or √30.
About this calculator
Formula and rules last checked 25 October 2026Written and tested by the CalculatorDex teamReport a problem