# What's the cube root of a number?

The cube root of a number n (³√n) is that figure which cubed (i.e. multiplied by itself twice) gives n.

Remember ³√ is the cube root symbol.

If n is a cube number (perfect cube) (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 etc), its cube root is a whole number.

But if n is a non-cube number (2, 3, 4, 5, 6, 7, 9, 10, 11, 12 etc), its cube root is a decimal and less easy to calculate.

Let's consider the cube roots of cube numbers first.

## How to work out the cube root of 1

Which figure cubed (times by itself twice) gives 1?

1³   =   1  x  1  x  1   =   1

Therefore ## Cube root of 8

What figure cubed (multiplied by itself twice) gives 8?

2³   =   2  x  2  x  2   =   8

So ## Cube root of 27

Which figure cubed (times by itself twice) gives 27?

3³   =   3  x  3  x  3   =   27

So ## Now what are the cube roots of the remaining cube numbers up to 1000?

The workings out are as follows

• ³64 = 4  (4³ = 4 x 4 x 4 = 64)
• ³125 = 5  (5³ = 5 x 5 x 5 = 125)
• ³216 = 6  (6³ = 6 x 6 x 6 = 216)
• ³343 = 7  (7³ = 7 x 7 x 7 = 343)
• ³512 = 8  (8³ = 8 x 8 x 8 = 512)
• ³729 = 9  (9³ = 9 x 9 x 9 = 729)
• ³1000 = 10  (10³ = 10 x 10 x 10 = 1000)

Notice all these cube roots are whole numbers.

## Next take a look at the cube roots of non-cube numbers

On your calculator, enter 2 followed by the cube root (³) button - you may need to press a shift or 2nd function key to access ³

The result is

1.25992105

You've calculated ³√2 - the cube root of 2.

It's a decimal, as are the cube roots of other non-cube numbers. For example, use your calculator to check the following

• ³√3   =   1.44224957
• ³√4   =   1.587401052
• ³√5   =   1.709975947
• ³√6   =   1.817120593
• ³√7   =   1.912931183
• ³√9   =   2.080083823
• ³√10   =   2.15443469
• ³√11   =   2.223980091
• ³√12   =   2.289428485

## Feeling more confident about cube roots?

After reading carefully through the examples provided in this lesson, you should now be able to work out cube roots regardless of whether they're whole numbers or decimals - albeit sometimes using your calculator!

For related topics click:

Square numbers