In these lessons, we will learn what are perfect cubes and how to calculate the cube root of 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, …
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.
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.
It is easy to work out the cube root of a perfect cube, but it is hard to work out other cube roots.
What is the smallest positive whole number that is a perfect cube and is a multiple of 24?
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