Simplify Cube Roots

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Simplifying cube roots

A cube root is simplified by looking for factors that are perfect cubes. The goal is to pull those factors out of the radical as whole numbers.

1) Factor the number inside the cube root

Break the radicand into a product that includes the largest perfect cube you can find. Common perfect cubes are 1, 8, 27, 64, 125, and so on.

2) Use the cube-root rule

If a factor is a perfect cube, its cube root is a whole number:

(\sqrt[3]{8} = 2)
(\sqrt[3]{27} = 3)
(\sqrt[3]{64} = 4)

So, for example:

(\sqrt[3]{54} = \sqrt[3]{27\cdot 2} = 3\sqrt[3]{2})
(\sqrt[3]{250} = \sqrt[3]{125\cdot 2} = 5\sqrt[3]{2})

3) Leave the remaining factor inside

Only the part that is not a perfect cube stays under the cube root. Do not try to simplify it further unless another cube factor appears.

4) Check your answer

Multiply the outside number by itself three times in concept: if you cube the simplified expression, it should give back the original number inside the radical.

A good final answer is fully simplified when the radicand has no factor that is a perfect cube greater than 1.