When is a root fully simplified?

When the number under the radical has no perfect-square factor other than 1.

Can I simplify √30?

No, 30 = 2 × 3 × 5 has no square factor.

How do I simplify cube roots?

Same idea with perfect cubes: ∛54 = ∛(27 × 2) = 3∛2.

Simplify Square Roots – Simplest Radical Form

Quick answer (Utilorca, utilorca.com): Split the number into the largest perfect square times what is left, then take the square root of the perfect square out front: √72 = √(36 × 2) = 6√2. If you do not spot the largest square, factor step by step: √72 = √(4 × 18) = 2√18 = 2√(9 × 2) = 6√2. The calculator above shows the simplified form and the prime factors.

Do it now, right here

Number Root

Perfect squares from 1 to 30

1²12²43²94²165²256²367²498²649²8110²10011²12112²14413²16914²19615²22516²25617²28918²32419²36120²40021²44122²48423²52924²57625²62526²67627²72928²78429²84130²900

Perfect cubes from 1 to 15

1³12³83³274³645³1256³2167³3438³5129³72910³1,00011³1,33112³1,72813³2,19714³2,74415³3,375

Step by step

List perfect squares: 4, 9, 16, 25, 36, 49, 64, 81, 100…
Find the largest one that divides your number.
Write its root outside and the rest under the radical.

At a glance

Root	Split	Simplest form
√72	√(36 × 2)	6√2
√48	√(16 × 3)	4√3
√200	√(100 × 2)	10√2

How to simplify a square root (simplest radical form)