Simplify Cube Root Calculator

Background.

A cube root asks which number, used three times as a factor, produces the number under the radical sign. For 27 or 1,000 the answer is a whole number. For 54 it is not — ∛54 is about 3.7798, an irrational decimal that never ends or repeats — but it can still be written exactly in a tidier form: 3∛2.

The tidying works because 54 hides a perfect cube. It equals 27 × 2, and the cube root of a product splits into the product of the cube roots, so ∛54 = ∛27 × ∛2 = 3∛2. Simplifying any cube root means finding every perfect-cube factor of the radicand, taking its cube root outside, and leaving behind the part with no cube factors left.

Grouping prime factors in threes is the dependable way to do it by hand. Written out, 432 is 2 × 2 × 2 × 2 × 3 × 3 × 3: one triple of 2s and one triple of 3s come out as 2 × 3 = 6, and the stray 2 stays inside, giving 6∛2. A pair is not enough. 72 is 2³ × 3², so only the 2 escapes and the answer is 2∛9 — this is where cube roots part company with square roots, in which 3² would have come straight out.

The simplified form is what algebra courses expect in a final answer, and it is what makes like terms visible: ∛54 + ∛16 looks stuck until both become multiples of ∛2, at which point the sum is simply 5∛2.

The page handles positive whole numbers up to one billion. Negative radicands, fractions, decimals and algebraic expressions such as ∛(16x⁴) are outside its range, though the first three can usually be rewritten to fit.

What is simplify cube root calculator?

Simplifying a cube root means rewriting ∛n as a∛b, where a and b are whole numbers, a³ × b = n, and b has no factor that is a perfect cube other than 1. This simplest radical form is unique for every positive integer. When n is itself a perfect cube, b is 1 and the root is just the whole number a; when n has no cube factors at all, a is 1 and the root is already in its simplest form.

How to use this calculator.

1. 01Enter the radicand, the number under the cube-root sign, as a positive whole number up to 1,000,000,000.
2. 02For a negative radicand, enter its absolute value and put a minus sign in front of the answer, since ∛(−54) = −∛54 = −3∛2.
3. 03Read the outside coefficient and remaining radicand together. The simplified form shows them as a cubert(b), the plain-text way of writing a∛b.
4. 04If the remaining radicand is 1, your number was a perfect cube and the coefficient is its exact cube root; if the coefficient is 1, the root cannot be simplified.

The formula.

The rule is ∛(a³ × b) = a∛b, which follows from ∛(xy) = ∛x × ∛y and ∛(a³) = a. To apply it, each whole number f is tried in turn, starting at 2, for as long as f³ does not exceed what is left of the radicand. Whenever f³ divides the remainder exactly, f is multiplied into the outside coefficient and the remainder is divided by f³; the same f is then tried again, so repeated cube factors such as 2⁶ are removed completely. Composite values of f never succeed, because their prime factors have already been stripped out by the time they are reached. The search ends once f³ exceeds the remainder, which guarantees no cube factor is left behind. Even at the one-billion limit, f never has to go past 1,000.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.