Radical Calculator

Simplify a radical such as √72 or ∛54 into simplest radical form, and see its decimal value and the factor steps.

How to simplify a radical

  1. Factor the number under the root (the radicand).
  2. Group factors into sets the size of the index: pairs for square roots, triples for cube roots.
  3. Move one copy of each complete set outside the radical.
  4. Leave the remaining factors inside.

Worked examples

∛54 = ∛(27 × 2) = 3∛2, because 27 = 3³. √72 = √(36 × 2) = 6√2.

Radical rules

RuleExample
√a × √b = √(ab)√2 × √8 = √16 = 4
√(a ÷ b) = √a ÷ √b√(9/4) = 3/2
ⁿ√(aⁿ) = a∛125 = 5
ⁿ√a = a^(1/n)√x = x^(1/2)

Frequently asked questions

What does simplest radical form mean?

No perfect square (or cube, for cube roots) factors remain under the radical, and there are no radicals in a denominator.

Can I take the cube root of a negative number?

Yes. Odd roots of negative numbers are real: ∛−8 = −2.

How do I add radicals?

Only like radicals can be added: 2√3 + 5√3 = 7√3. Simplify first to find like terms.

What is the index of a radical?

The small number on the root sign that tells you which root to take. A plain √ has index 2.

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