∛ Simplify Cube Root Calculator

Simplify Cube Root Calculator

Use the calculator above to simplify any cube root to its simplest radical form (e.g. ∛24 = 2∛3). See below the step-by-step method using prime factorization, plus a table of common simplified cube roots.

Formula

To rewrite any cube root in simplest radical form:

∛(a³ · b) = a · ∛b

Where:

• a³ = the largest perfect-cube factor of the radicand (the number under the ∛ symbol)
• b = the remaining cubefree factor (no perfect cube divides it other than 1)

Worked example for ∛24:

• 24 = 8 × 3 = 2³ × 3
• So a³ = 8, a = 2, b = 3
• Therefore ∛24 = 2∛3

How to Simplify Cube Roots

Simplifying a cube root means rewriting it in the simplest radical form, where the number under the radical (the radicand) has no perfect cube factors other than 1.

Method: Prime Factorization

1. Find the prime factorization of the radicand.
2. Identify triples (groups of three) of identical prime factors.
3. Each complete triple contributes one factor outside the radical.
4. Any prime factor not part of a complete triple (1 or 2 leftovers) stays under the radical.

Example: Simplify ∛128

1. 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁷
2. We have two complete triples of 2's (2³ × 2³) plus a leftover 2.
3. Each triple → contributes one 2 outside. Two triples → 2 × 2 = 4 outside. The leftover 2 stays inside.
4. ∛128 = 4∛2

Common Simplified Cube Roots

Click any value to see the full step-by-step solution.

References

• [1] Simplified form of a radical expression (Wikipedia)
• [2] Cube root (Wikipedia)

Popular Simplified Cube Roots

Top cube root simplifications — click any to see the step-by-step solution: