Cube Roots

Cube Roots

To understand cube roots, let's first review how to cube a number.  The expression "three cubed" can be written as 33.  And we already know that this can be written as 3 x 3 x 3 or 27.  Six cubed can be written as 63, 6 x 6 x 6 or 216.

A cube root is essentially going in the reverse direction.  The cube root of 27 is 3, and the cube root of 216 is 6.  When you are asked what the cube root of a number x is, you need to find the number that can be multiplied by itself 3 times to equal x.

If you are trying to find the cube root of 27, it is usually written like this:

The cube root of 216 is written like this:

These numbers are called perfect cubes because the answer is a whole number.

What if you are asked to find the cube root of 35, or   ? We know that 3 cubed equals 27 and 4 cubed (4 x 4 x 4) equals 64.  So the cube root of 35 is between 3 and 4.  For a more exact answer, try using your calculator.

Example:

We know that 4 cubed is 64.  So 5 would be a good place to start. 5 times 5 is 25, times 5 again is 125.  And we have our answer!