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Exponents

The Cube Root

The cube root is the reverse operation of cubing a number.

Example

23 = 8,  so 2 is a cube root of 8.

(-2)3 = -8,  so -2 is a cube root of -8.

 

3 =   , so  is a cube root of .

3 =  , so  is a cube root of .

As you can see, all numbers have a unique cube root.

The cube root of a positive number b is denoted by cube root of b  or b^(1/3)   (See nth root for more on fractional notation) and the cube root of a negative number -b is cube root of -b = - cube root of b .

 

The graph of x3 is shown below. From the graph we can clearly see that each positive number will have a positive cube root, and each negative number will have a negative cube root.

graph of cube root of b.

 

 

Now try a few on your own.

Exercise

If the cube root of b is an integer, display it in the box provided; otherwise type NI for "not integer".

b
cube root of b

<< Square Root | Exponents Index | nth Root >>

 

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