In these lessons, we will learn what are perfect cubes and how to calculate the cube root of a perfect cube.

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### What Is A Perfect Cube?

A perfect cube is a number that is the **cube of an integer**.

For example, 125 is a perfect cube since 125 = 5 × 5 × 5 = 53

Some other examples of perfect cubes are 1, 8, 27, 64, 125, 216, 343, …

### What Is A Cube Root?

The opposite of cubing a number is finding the cube root. Since 53 = 125, the cube root of 125 is 5. The cube root of a perfect cube is an integer.

It is possible to get the cube root of a negative number. For example, the cube root of −125 is −5 since (−5) × (−5) × (−5) = −125.

The following table shows some perfect cubes and cube roots. Scroll down the page for more examples of how to evaluate cube root of perfect cubes.

Perfect Cubes & Cube RootsEvaluate Square Roots Of Perfect Squares And Cube Roots Of Perfect Cubes How To Simplify Radicals With Negative Radicands And Odd Indexes? Perfect Cubes And Cube Roots

To cube a number, we use the number in a multiplication 3 times. For example, 4 cubed = 43 = 4 × 4 × 4 = 64

A cube root goes the other direction. 3 cubed is 27, so the cube root of 27 is 3.

The cube root of a number is the value that when cubed gives the original number.The cube root of 27 is 3 because when 3 is cubed you get 27.

∛ is the special symbol that means “cube root”. It is the radical symbol √ with a little three to mean cube root.You can use it like this:∛27 = 3.

Perfect cubes are cubes of whole numbers.

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It is easy to work out the cube root of a perfect cube, but it is hard to work out other cube roots.

How To Find The Smallest Multiple Of Another Number That Is Also A Perfect Cube?**Example:**What is the smallest positive whole number that is a perfect cube and is a multiple of 24?

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